%------------------------------------------------------------------------------
% File     : SCT170_30 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Social Choice Theory
% Problem  : Arrow's Impossibility Theorem line 204, 1000 axioms selected
% Version  : SCT170_3 with the conjecture removed
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [TPTP]
% Names    : 

% Status   : Satisfiable
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    : 2968 ( 342 unt;1624 typ;   0 def)
%            Number of atoms       : 3304 ( 927 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 2397 ( 437   ~;  86   |; 167   &)
%                                         ( 223 <=>;1484  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :   19 (   2 avg)
%            Number of types       :  604 ( 603 usr)
%            Number of type conns  : 1211 ( 644   >; 567   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    : 1020 (1020 usr; 377 con; 0-2 aty)
%            Number of variables   : 4003 (3807   !; 196   ?;4003   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:36:54
%------------------------------------------------------------------------------
%----Should-be-implicit typings (603)
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tff(sy_c_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat,type,
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tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__,type,
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tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___436,type,
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tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___437,type,
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tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___438,type,
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tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng,type,
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tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_439,type,
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tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_440,type,
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tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_441,type,
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tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_442,type,
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tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_443,type,
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tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
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tff(sy_c_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_,type,
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tff(sy_c_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__444,type,
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tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_445,type,
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tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_446,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__Arrow__,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__List__O,type,
    cOMBC_673369480le_alt: fun_fu1574695223le_alt ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc_447,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc_448,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__Arrow_,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__Arrow__449,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__Arrow__450,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_It,type,
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tff(sy_c_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool,type,
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tff(sy_c_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa_451,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa_452,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa_453,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__H,type,
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tff(sy_c_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_,type,
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tff(sy_c_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__454,type,
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tff(sy_c_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
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tff(sy_c_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_455,type,
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tff(sy_c_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
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tff(sy_c_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___456,type,
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tff(sy_c_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_,type,
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tff(sy_c_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__457,type,
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tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_458,type,
    cOMBC_2103205814t_bool: fun_fu1798685131t_bool ).

tff(sy_c_COMBI_000tc__Nat__Onat,type,
    cOMBI_nat: fun_nat_nat ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
    cOMBK_2077209654le_alt: fun_bo473319367t_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____effngqiqbs__O_459,type,
    cOMBK_561380029e_indi: fun_bo1933551930i_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Nat__Onat,type,
    cOMBK_bool_nat: fun_bo1570548802t_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____eff,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___460,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___461,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___462,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__463,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__464,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__465,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow___,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_Itc__Arrow__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,type,
    cOMBK_2008571104t_bool: fun_fu370172154t_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__prod_Itc__Arrow___,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_466,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_467,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_468,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_469,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn_470,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn_471,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn_472,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn_473,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_474,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_475,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_476,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_477,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_478,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___479,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___480,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___481,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___482,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_483,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_484,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_485,type,
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tff(sy_c_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
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tff(sy_c_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa_486,type,
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tff(sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t,type,
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tff(sy_c_FunDef_Oin__rel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__f,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__f_487,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__f_488,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__p,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc___489,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc___491,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle__,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____M,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle_,type,
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tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle___,type,
    pi_nat1489913205t_bool: ( fun_nat_bool * fun_na6909291l_bool ) > fun_fu1994743771l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mir,type,
    pi_nat608045987t_bool: ( fun_nat_bool * fun_na138495129l_bool ) > fun_fu734766857l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mi,type,
    pi_nat1942897898t_bool: ( fun_nat_bool * fun_na144630978l_bool ) > fun_fu1197928274l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__prod_Itc__Arrow____Order____Mirabelle__,type,
    pi_nat140973286le_alt: ( fun_nat_bool * fun_na998785244t_bool ) > fun_fu1000784716t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind,type,
    pi_fun1760679520le_alt: ( fun_fu3835832l_bool * fun_fu2143707488t_bool ) > fun_fu1360221516t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_492,type,
    pi_fun520512275e_indi: ( fun_fu3835832l_bool * fun_fu223278561i_bool ) > fun_fu1864062453i_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_493,type,
    pi_fun853738700l_bool: ( fun_fu3835832l_bool * fun_fu916327706l_bool ) > fun_fu1370139438l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_494,type,
    pi_fun614388187ol_nat: ( fun_fu3835832l_bool * fun_fu1077134171t_bool ) > fun_fu1313929543t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_495,type,
    pi_fun1746584570t_bool: ( fun_fu3835832l_bool * fun_fu1863781882l_bool ) > fun_fu2098777574l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_496,type,
    pi_fun645774662le_alt: ( fun_fu3835832l_bool * fun_fu1258557076t_bool ) > fun_fu1832644776t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi,type,
    pi_fun1429765554le_alt: ( fun_fu2098777574l_bool * fun_fu1566951310t_bool ) > fun_fu331160990t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi_497,type,
    pi_fun1807454273e_indi: ( fun_fu2098777574l_bool * fun_fu2109152051i_bool ) > fun_fu523608611i_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi_498,type,
    pi_fun1312540410l_bool: ( fun_fu2098777574l_bool * fun_fu1522163052l_bool ) > fun_fu1992232028l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi_499,type,
    pi_fun1997317165ol_nat: ( fun_fu2098777574l_bool * fun_fu1667513993t_bool ) > fun_fu1395354777t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi_500,type,
    pi_fun294122868le_alt: ( fun_fu2098777574l_bool * fun_fu2050451686t_bool ) > fun_fu1260701654t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq,type,
    pi_fun1511699953le_alt: ( fun_fu638310559l_bool * fun_fu1534804551t_bool ) > fun_fu74552793t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq_501,type,
    pi_fun1470523330e_indi: ( fun_fu638310559l_bool * fun_fu2142850746i_bool ) > fun_fu1406810280i_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq_502,type,
    pi_fun1035089915l_bool: ( fun_fu638310559l_bool * fun_fu237781875l_bool ) > fun_fu2013733473l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq_503,type,
    pi_fun476373740ol_nat: ( fun_fu638310559l_bool * fun_fu477456066t_bool ) > fun_fu1491371348t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq_504,type,
    pi_fun34562933le_alt: ( fun_fu638310559l_bool * fun_fu1924348397t_bool ) > fun_fu1310641883t_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal,type,
    pi_Pro262333359le_alt: ( fun_Pr2067565481t_bool * fun_Pr1407669585t_bool ) > fun_fu1649663259t_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_505,type,
    pi_Pro837265796e_indi: ( fun_Pr2067565481t_bool * fun_Pr895221296i_bool ) > fun_fu902545894i_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_506,type,
    pi_Pro1238944957t_bool: ( fun_Pr2067565481t_bool * fun_Pr1780397033l_bool ) > fun_fu638310559l_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_507,type,
    pi_Pro847445418lt_nat: ( fun_Pr2067565481t_bool * fun_Pr428964044t_bool ) > fun_fu1377329046t_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_508,type,
    pi_Pro910144055le_alt: ( fun_Pr2067565481t_bool * fun_Pr1701595235t_bool ) > fun_fu507038489t_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,
    pi_Pro606697670t_bool: ( fun_Pr486337689t_bool * fun_Pr1204542610l_bool ) > fun_fu1570026792l_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___509,type,
    pi_Pro87132148t_bool: ( fun_Pr486337689t_bool * fun_Pr1411261120l_bool ) > fun_fu898064726l_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___510,type,
    pi_Pro469835097t_bool: ( fun_Pr486337689t_bool * fun_Pr80661467l_bool ) > fun_fu2729669l_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___511,type,
    pi_Pro1151594295le_alt: ( fun_Pr486337689t_bool * fun_Pr324456707t_bool ) > fun_fu765977497t_bool ).

tff(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
    minus_minus_nat: nat > fun_nat_nat ).

tff(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
    one_one_nat: nat ).

tff(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
    plus_plus_nat: nat > fun_nat_nat ).

tff(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
    zero_zero_nat: nat ).

tff(sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
    equal_631514850le_alt: fun_li495175091t_bool ).

tff(sy_c_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqi,type,
    if_Pro1687484775le_alt: bool > fun_Pr544315117le_alt ).

tff(sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    append1597383892le_alt: fun_li264309018le_alt ).

tff(sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    append139047327e_indi: fun_li1386059829e_indi ).

tff(sy_c_List_Oappend_000tc__HOL__Obool,type,
    append_bool: fun_li662746748t_bool ).

tff(sy_c_List_Oappend_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqi,type,
    append1312904639le_alt: fun_li485644309le_alt ).

tff(sy_c_List_Oappend_000tc__Nat__Onat,type,
    append_nat: fun_li511653589st_nat ).

tff(sy_c_List_Oappend_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin,type,
    append20579569t_bool: fun_li482685923t_bool ).

tff(sy_c_List_Oappend_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
    append34563871t_bool: fun_li1021842101t_bool ).

tff(sy_c_List_Oappend_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effng,type,
    append1496262254t_bool: fun_li633046836t_bool ).

tff(sy_c_List_Oappend_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
    append200898658le_alt: fun_li1077448946le_alt ).

tff(sy_c_List_Oappend_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    append1796561362le_alt: fun_li375927042le_alt ).

tff(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    butlas1693249291le_alt: fun_li90789869le_alt ).

tff(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    butlas981234984e_indi: fun_li651424637e_indi ).

tff(sy_c_List_Obutlast_000tc__HOL__Obool,type,
    butlast_bool: fun_li107039421t_bool ).

tff(sy_c_List_Obutlast_000tc__Nat__Onat,type,
    butlast_nat: fun_li1155097699st_nat ).

tff(sy_c_List_Obutlast_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oi,type,
    butlas481790330t_bool: fun_li1129981181t_bool ).

tff(sy_c_List_Obutlast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effng,type,
    butlas1125166248t_bool: fun_li1328417149t_bool ).

tff(sy_c_List_Obutlast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effn,type,
    butlas1729912741t_bool: fun_li1539627809t_bool ).

tff(sy_c_List_Obutlast_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
    butlas1780591595le_alt: fun_li1098897981le_alt ).

tff(sy_c_List_Obutlast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle,type,
    butlas1837197275le_alt: fun_li262510141le_alt ).

tff(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    distin1654625714le_alt: fun_li1109619974t_bool ).

tff(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    distin1343912001e_indi: fun_li1640834235i_bool ).

tff(sy_c_List_Odistinct_000tc__HOL__Obool,type,
    distinct_bool: fun_list_bool_bool ).

tff(sy_c_List_Odistinct_000tc__Nat__Onat,type,
    distinct_nat: fun_list_nat_bool ).

tff(sy_c_List_Odistinct_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
    distin194731411t_bool: fun_li764922637l_bool ).

tff(sy_c_List_Odistinct_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn,type,
    distin1644384705t_bool: fun_li1841738811l_bool ).

tff(sy_c_List_Odistinct_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff,type,
    distin116221260t_bool: fun_li2047702944l_bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    distin748429060le_alt: fun_li2133552254t_bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
    distin1934286196le_alt: fun_li154183278t_bool ).

tff(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    dropWh587599712le_alt: fun_Ar17477381t_bool > fun_li90789869le_alt ).

tff(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    dropWh587229715e_indi: fun_Ar1809396326i_bool > fun_li651424637e_indi ).

tff(sy_c_List_OdropWhile_000tc__HOL__Obool,type,
    dropWhile_bool: fun_bool_bool > fun_li107039421t_bool ).

tff(sy_c_List_OdropWhile_000tc__Nat__Onat,type,
    dropWhile_nat: fun_nat_bool > fun_li1155097699st_nat ).

tff(sy_c_List_OdropWhile_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    dropWh1724617061t_bool: fun_fu3835832l_bool > fun_li1129981181t_bool ).

tff(sy_c_List_OdropWhile_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,type,
    dropWh1823459219t_bool: fun_fu2098777574l_bool > fun_li1328417149t_bool ).

tff(sy_c_List_OdropWhile_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,type,
    dropWh1706032378t_bool: fun_fu638310559l_bool > fun_li1539627809t_bool ).

tff(sy_c_List_OdropWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    dropWh1799418070le_alt: fun_Pr2067565481t_bool > fun_li1098897981le_alt ).

tff(sy_c_List_OdropWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    dropWh1985299526le_alt: fun_Pr486337689t_bool > fun_li262510141le_alt ).

tff(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    drop_A617527551le_alt: fun_na960272160le_alt ).

tff(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    drop_A1023486004e_indi: fun_na2132534960e_indi ).

tff(sy_c_List_Odrop_000tc__HOL__Obool,type,
    drop_bool: fun_na1279735280t_bool ).

tff(sy_c_List_Odrop_000tc__Nat__Onat,type,
    drop_nat: fun_na941842582st_nat ).

tff(sy_c_List_Odrop_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    drop_f1253107846t_bool: fun_na1637148720t_bool ).

tff(sy_c_List_Odrop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiq,type,
    drop_f1976219572t_bool: fun_na802299056t_bool ).

tff(sy_c_List_Odrop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqi,type,
    drop_f1214627225t_bool: fun_na1396592724t_bool ).

tff(sy_c_List_Odrop_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    drop_P2052955895le_alt: fun_na794783088le_alt ).

tff(sy_c_List_Odrop_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    drop_P663726311le_alt: fun_na190419312le_alt ).

tff(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    hd_Arr1236501138le_alt: list_A114658244le_alt > arrow_1893660431le_alt ).

tff(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    hd_Arr451003233e_indi: list_A270647749e_indi > arrow_856714788e_indi ).

tff(sy_c_List_Ohd_000tc__HOL__Obool,type,
    hd_bool: list_bool > bool ).

tff(sy_c_List_Ohd_000tc__Nat__Onat,type,
    hd_nat: list_nat > nat ).

tff(sy_c_List_Ohd_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_M,type,
    hd_fun449104051t_bool: list_f1976315671t_bool > fun_Ar274636406t_bool ).

tff(sy_c_List_Ohd_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs,type,
    hd_fun1991171297t_bool: list_f1981087045t_bool > fun_fu2114379172t_bool ).

tff(sy_c_List_Ohd_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqb,type,
    hd_fun1302671916t_bool: list_f733367646t_bool > fun_Pr2067565481t_bool ).

tff(sy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_M,type,
    hd_Pro1416718884le_alt: list_P1419683592le_alt > produc472769767le_alt ).

tff(sy_c_List_Ohd_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____e,type,
    hd_Pro82081940le_alt: list_P662130680le_alt > produc587761367le_alt ).

tff(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    insert1391384533le_alt: fun_Ar1448189019le_alt ).

tff(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    insert901693150e_indi: fun_Ar240957002e_indi ).

tff(sy_c_List_Oinsert_000tc__HOL__Obool,type,
    insert_bool: fun_bo1175651857t_bool ).

tff(sy_c_List_Oinsert_000tc__Nat__Onat,type,
    insert_nat: fun_na941842582st_nat ).

tff(sy_c_List_Oinsert_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin,type,
    insert1837816112t_bool: fun_fu5455096t_bool ).

tff(sy_c_List_Oinsert_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
    insert1598751326t_bool: fun_fu1327618250t_bool ).

tff(sy_c_List_Oinsert_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effng,type,
    insert774660719t_bool: fun_fu1477494133t_bool ).

tff(sy_c_List_Oinsert_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
    insert148673953le_alt: fun_Pr174382471le_alt ).

tff(sy_c_List_Oinsert_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    insert559460497le_alt: fun_Pr1418635159le_alt ).

tff(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    last_A488133080le_alt: list_A114658244le_alt > arrow_1893660431le_alt ).

tff(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    last_A1878443419e_indi: list_A270647749e_indi > arrow_856714788e_indi ).

tff(sy_c_List_Olast_000tc__HOL__Obool,type,
    last_bool: list_bool > bool ).

tff(sy_c_List_Olast_000tc__Nat__Onat,type,
    last_nat: list_nat > nat ).

tff(sy_c_List_Olast_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    last_f1589458157t_bool: list_f1976315671t_bool > fun_Ar274636406t_bool ).

tff(sy_c_List_Olast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiq,type,
    last_f1285862171t_bool: list_f1981087045t_bool > fun_fu2114379172t_bool ).

tff(sy_c_List_Olast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqi,type,
    last_f537687922t_bool: list_f733367646t_bool > fun_Pr2067565481t_bool ).

tff(sy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    last_P628018270le_alt: list_P1419683592le_alt > produc472769767le_alt ).

tff(sy_c_List_Olast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    last_P1104483278le_alt: list_P662130680le_alt > produc587761367le_alt ).

tff(sy_c_List_Olex_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    lex_Ar686335011le_alt: fun_fu1924348397t_bool ).

tff(sy_c_List_Olex_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs,type,
    lex_li810040752le_alt: fun_fu27751565t_bool ).

tff(sy_c_List_Olexn_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    lexn_A1588662879le_alt: ( fun_Pr2067565481t_bool * nat ) > fun_Pr486337689t_bool ).

tff(sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    lexord228913196le_alt: fun_fu1924348397t_bool ).

tff(sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    lexord1088797767e_indi: fun_fu1298326093i_bool ).

tff(sy_c_List_Olexord_000tc__HOL__Obool,type,
    lexord_bool: fun_fu567784347l_bool ).

tff(sy_c_List_Olexord_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqi,type,
    lexord616819815le_alt: fun_fu27751565t_bool ).

tff(sy_c_List_Olexord_000tc__Nat__Onat,type,
    lexord_nat: fun_fu55128739t_bool ).

tff(sy_c_List_Olexord_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin,type,
    lexord41383833t_bool: fun_fu1062071593l_bool ).

tff(sy_c_List_Olexord_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
    lexord1846952391t_bool: fun_fu1111780685l_bool ).

tff(sy_c_List_Olexord_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effng,type,
    lexord1057491398t_bool: fun_fu1812375457l_bool ).

tff(sy_c_List_Olexord_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
    lexord1620771594le_alt: fun_fu1132264071t_bool ).

tff(sy_c_List_Olexord_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    lexord198649978le_alt: fun_fu399958567t_bool ).

tff(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    cons_A1647044463le_alt: fun_Ar1448189019le_alt ).

tff(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    cons_A90150340e_indi: fun_Ar240957002e_indi ).

tff(sy_c_List_Olist_OCons_000tc__HOL__Obool,type,
    cons_bool: fun_bo1175651857t_bool ).

tff(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____eff,type,
    cons_l782000996le_alt: fun_li638184490le_alt ).

tff(sy_c_List_Olist_OCons_000tc__Nat__Onat,type,
    cons_nat: fun_na941842582st_nat ).

tff(sy_c_List_Olist_OCons_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    cons_f1976067606t_bool: fun_fu5455096t_bool ).

tff(sy_c_List_Olist_OCons_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ef,type,
    cons_f1814775108t_bool: fun_fu1327618250t_bool ).

tff(sy_c_List_Olist_OCons_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____e,type,
    cons_f1988942857t_bool: fun_fu1477494133t_bool ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs,type,
    cons_P885197959le_alt: fun_Pr174382471le_alt ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,
    cons_P1273708151le_alt: fun_Pr1418635159le_alt ).

tff(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    nil_Ar557011903le_alt: list_A114658244le_alt ).

tff(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    nil_Ar1954758004e_indi: list_A270647749e_indi ).

tff(sy_c_List_Olist_ONil_000tc__HOL__Obool,type,
    nil_bool: list_bool ).

tff(sy_c_List_Olist_ONil_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,type,
    nil_li2054189844le_alt: list_l2028444773le_alt ).

tff(sy_c_List_Olist_ONil_000tc__Nat__Onat,type,
    nil_nat: list_nat ).

tff(sy_c_List_Olist_ONil_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    nil_fu2063482310t_bool: list_f1976315671t_bool ).

tff(sy_c_List_Olist_ONil_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,type,
    nil_fu1881361652t_bool: list_f1981087045t_bool ).

tff(sy_c_List_Olist_ONil_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,type,
    nil_fu1079711833t_bool: list_f733367646t_bool ).

tff(sy_c_List_Olist_ONil_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    nil_Pr1980478519le_alt: list_P1419683592le_alt ).

tff(sy_c_List_Olist_ONil_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    nil_Pr1738530343le_alt: list_P662130680le_alt ).

tff(sy_c_List_Olist_Olist__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    list_c1024366775le_alt: ( list_A114658244le_alt * fun_Ar1448189019le_alt ) > fun_li90789869le_alt ).

tff(sy_c_List_Olist__update_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    list_u1480779303le_alt: list_A114658244le_alt > fun_na1003310479le_alt ).

tff(sy_c_List_Olistrel1_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    listre1334820888le_alt: fun_fu1924348397t_bool ).

tff(sy_c_List_Olistrel1_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effng,type,
    listre767458683le_alt: fun_fu27751565t_bool ).

tff(sy_c_List_Olistrel_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    listre1191473383le_alt: fun_fu1924348397t_bool ).

tff(sy_c_List_Olistrel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngq,type,
    listre770069484le_alt: fun_fu27751565t_bool ).

tff(sy_c_List_Olistrelp_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    listre483979801le_alt: fun_Ar331856045t_bool > fun_li495175091t_bool ).

tff(sy_c_List_Olistrelp_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effng,type,
    listre963584058le_alt: fun_li495175091t_bool > fun_li1489248217t_bool ).

tff(sy_c_List_Omaps_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__Ar,type,
    maps_A652163713le_alt: fun_Ar849108972le_alt > fun_li90789869le_alt ).

tff(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    null_A791782855le_alt: fun_li1109619974t_bool ).

tff(sy_c_List_Opartition_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    partit758395576le_alt: ( fun_Ar17477381t_bool * list_A114658244le_alt ) > produc587761367le_alt ).

tff(sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    replic782356601le_alt: nat > fun_Ar849108972le_alt ).

tff(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    rev_Ar377224735le_alt: fun_li90789869le_alt ).

tff(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    rev_Ar2076519188e_indi: fun_li651424637e_indi ).

tff(sy_c_List_Orev_000tc__HOL__Obool,type,
    rev_bool: fun_li107039421t_bool ).

tff(sy_c_List_Orev_000tc__Nat__Onat,type,
    rev_nat: fun_li1155097699st_nat ).

tff(sy_c_List_Orev_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_,type,
    rev_fu2129709926t_bool: fun_li1129981181t_bool ).

tff(sy_c_List_Orev_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqb,type,
    rev_fu1281784468t_bool: fun_li1328417149t_bool ).

tff(sy_c_List_Orev_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq,type,
    rev_fu1613832889t_bool: fun_li1539627809t_bool ).

tff(sy_c_List_Orev_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_,type,
    rev_Pr187933143le_alt: fun_li1098897981le_alt ).

tff(sy_c_List_Orev_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    rev_Pr844913607le_alt: fun_li262510141le_alt ).

tff(sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    rotate1753650700le_alt: fun_li90789869le_alt ).

tff(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    set_Ar1995755744le_alt: list_A114658244le_alt > fun_Ar17477381t_bool ).

tff(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    set_Ar205654163e_indi: list_A270647749e_indi > fun_Ar1809396326i_bool ).

tff(sy_c_List_Oset_000tc__HOL__Obool,type,
    set_bool: list_bool > fun_bool_bool ).

tff(sy_c_List_Oset_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs,type,
    set_li1778885299le_alt: list_l2028444773le_alt > fun_li1109619974t_bool ).

tff(sy_c_List_Oset_000tc__Nat__Onat,type,
    set_nat: list_nat > fun_nat_bool ).

tff(sy_c_List_Oset_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_,type,
    set_fu2037886949t_bool: list_f1976315671t_bool > fun_fu3835832l_bool ).

tff(sy_c_List_Oset_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqb,type,
    set_fu2135320083t_bool: list_f1981087045t_bool > fun_fu2098777574l_bool ).

tff(sy_c_List_Oset_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq,type,
    set_fu1957445242t_bool: list_f733367646t_bool > fun_fu638310559l_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_,type,
    set_Pr496668502le_alt: list_P1419683592le_alt > fun_Pr2067565481t_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    set_Pr1785012934le_alt: list_P662130680le_alt > fun_Pr486337689t_bool ).

tff(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    splice791716242le_alt: list_A114658244le_alt > fun_li90789869le_alt ).

tff(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    takeWh967109304le_alt: fun_Ar17477381t_bool > fun_li90789869le_alt ).

tff(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    takeWh259024059e_indi: fun_Ar1809396326i_bool > fun_li651424637e_indi ).

tff(sy_c_List_OtakeWhile_000tc__HOL__Obool,type,
    takeWhile_bool: fun_bool_bool > fun_li107039421t_bool ).

tff(sy_c_List_OtakeWhile_000tc__Nat__Onat,type,
    takeWhile_nat: fun_nat_bool > fun_li1155097699st_nat ).

tff(sy_c_List_OtakeWhile_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    takeWh1481438221t_bool: fun_fu3835832l_bool > fun_li1129981181t_bool ).

tff(sy_c_List_OtakeWhile_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,type,
    takeWh1969918523t_bool: fun_fu2098777574l_bool > fun_li1328417149t_bool ).

tff(sy_c_List_OtakeWhile_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,type,
    takeWh2085154898t_bool: fun_fu638310559l_bool > fun_li1539627809t_bool ).

tff(sy_c_List_OtakeWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    takeWh1421241214le_alt: fun_Pr2067565481t_bool > fun_li1098897981le_alt ).

tff(sy_c_List_OtakeWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    takeWh797115118le_alt: fun_Pr486337689t_bool > fun_li262510141le_alt ).

tff(sy_c_List_Otake_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    take_A2032349095le_alt: fun_na960272160le_alt ).

tff(sy_c_List_Otake_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    take_A1953651596e_indi: fun_na2132534960e_indi ).

tff(sy_c_List_Otake_000tc__HOL__Obool,type,
    take_bool: fun_na1279735280t_bool ).

tff(sy_c_List_Otake_000tc__Nat__Onat,type,
    take_nat: fun_na941842582st_nat ).

tff(sy_c_List_Otake_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    take_f1842263006t_bool: fun_na1637148720t_bool ).

tff(sy_c_List_Otake_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiq,type,
    take_f1080892172t_bool: fun_na802299056t_bool ).

tff(sy_c_List_Otake_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqi,type,
    take_f362945601t_bool: fun_na1396592724t_bool ).

tff(sy_c_List_Otake_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    take_P1172918863le_alt: fun_na794783088le_alt ).

tff(sy_c_List_Otake_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    take_P961419327le_alt: fun_na190419312le_alt ).

tff(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    tl_Arr1883752598le_alt: fun_li90789869le_alt ).

tff(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    tl_Arr1600323165e_indi: fun_li651424637e_indi ).

tff(sy_c_List_Otl_000tc__HOL__Obool,type,
    tl_bool: fun_li107039421t_bool ).

tff(sy_c_List_Otl_000tc__Nat__Onat,type,
    tl_nat: fun_li1155097699st_nat ).

tff(sy_c_List_Otl_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_M,type,
    tl_fun210444207t_bool: fun_li1129981181t_bool ).

tff(sy_c_List_Otl_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs,type,
    tl_fun66473949t_bool: fun_li1328417149t_bool ).

tff(sy_c_List_Otl_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqb,type,
    tl_fun496344112t_bool: fun_li1539627809t_bool ).

tff(sy_c_List_Otl_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_M,type,
    tl_Pro2051728672le_alt: fun_li1098897981le_alt ).

tff(sy_c_List_Otl_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____e,type,
    tl_Pro673569168le_alt: fun_li262510141le_alt ).

tff(sy_c_Nat_OSuc,type,
    suc: fun_nat_nat ).

tff(sy_c_Nat_Onat_Onat__case_000tc__HOL__Obool,type,
    nat_case_bool: ( bool * fun_nat_bool ) > fun_nat_bool ).

tff(sy_c_Nat_Onat_Onat__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    nat_ca146784400le_alt: ( list_A114658244le_alt * fun_na86871399le_alt ) > fun_na86871399le_alt ).

tff(sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat,type,
    nat_case_nat: ( nat * fun_nat_nat ) > fun_nat_nat ).

tff(sy_c_Nat_Onat_Onat__size,type,
    nat_size: fun_nat_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    size_s2005684270le_alt: fun_li1574574519lt_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Or,type,
    size_s317648763le_alt: fun_li1064136482lt_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__Nat__Onat,type,
    size_size_nat: fun_nat_nat ).

tff(sy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabel,type,
    order_1266734903le_alt: fun_Ar17477381t_bool > fun_fu638310559l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__HOL__Obool,type,
    ord_less_eq_bool: fun_bo1549164019l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle,type,
    ord_le1779845435t_bool: fun_fu1085384691l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle_512,type,
    ord_le1609180592i_bool: fun_fu924966107l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_,type,
    ord_le742797417l_bool: fun_fu1393819981l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    ord_le1568362934t_bool: fun_fu1217155507l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__Arrow____Order____,type,
    ord_le1099920642l_bool: fun_fu1785284735l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____,type,
    ord_le1121695024l_bool: fun_fu2060968923l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow___,type,
    ord_le1545885909l_bool: fun_fu1265985907l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Arrow____Order___,type,
    ord_le1577377523t_bool: fun_fu643206625l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc__,type,
    ord_le907370723t_bool: fun_fu1439151937l_bool ).

tff(sy_c_Orderings_Oord__class_Omin_000tc__Nat__Onat,type,
    ord_min_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,type,
    top_top_bool: bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____e,type,
    top_to814956427t_bool: fun_Ar17477381t_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____e_513,type,
    top_to788185952i_bool: fun_Ar1809396326i_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    top_to1647826457l_bool: fun_bool_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    top_top_fun_nat_bool: fun_nat_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirab,type,
    top_to553140914l_bool: fun_fu3835832l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order,type,
    top_to827110112l_bool: fun_fu2098777574l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Orde,type,
    top_to1312956197l_bool: fun_fu638310559l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mira,type,
    top_to1138392227t_bool: fun_Pr2067565481t_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow,type,
    top_to1339422355t_bool: fun_Pr486337689t_bool ).

tff(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_,type,
    produc1590937303le_alt: fun_Ar2121501495le_alt ).

tff(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    produc1408223885e_indi: fun_Ar1814172397e_indi ).

tff(sy_c_Product__Type_OPair_000tc__HOL__Obool_000tc__HOL__Obool,type,
    produc1246214911l_bool: fun_bo1175459231l_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    produc1742925389le_alt: fun_li380014893le_alt ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_____514,type,
    produc1006390615e_indi: fun_li1160816419e_indi ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__HOL__Obool_J_000tc__List__Olist,type,
    produc1067887767t_bool: fun_li998062677t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order,type,
    produc48145751le_alt: fun_li1998532451le_alt ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Nat__Onat_J_000tc__List__Olist_,type,
    produc1869962435st_nat: fun_li1596838627st_nat ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mira,type,
    produc1633570007t_bool: fun_li831465799t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Orde,type,
    produc836087127t_bool: fun_li1552454179t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Ord,type,
    produc2021583233t_bool: fun_li1459743457t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mir,type,
    produc214947223le_alt: fun_li946730985le_alt ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arro,type,
    produc1238470167le_alt: fun_li500450505le_alt ).

tff(sy_c_Product__Type_OPair_000tc__Nat__Onat_000tc__Nat__Onat,type,
    product_Pair_nat_nat: fun_na257798253at_nat ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiq,type,
    produc148697137t_bool: fun_fu1054990353t_bool ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle___,type,
    produc857581453t_bool: fun_fu1105896941t_bool ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle__,type,
    produc873875543t_bool: fun_fu1707827691t_bool ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqi,type,
    produc1036070419le_alt: fun_Pr1612123699le_alt ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mir,type,
    produc474284787le_alt: fun_Pr309696275le_alt ).

tff(sy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    produc410835390t_bool: fun_Pr2067565481t_bool > fun_Ar331856045t_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    produc1907517876t_bool: fun_Pr486337689t_bool > fun_li495175091t_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____515,type,
    produc1639868974le_alt: fun_Pr1186243091le_alt > fun_li380014893le_alt ).

tff(sy_c_Product__Type_Ointernal__split_000tc__Arrow____Order____Mirabelle____effngq,type,
    produc2015632596t_bool: fun_fu1428047277t_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Arrow____Order____Mi,type,
    produc1354545732le_alt: fun_fu736403735le_alt ).

tff(sy_c_Product__Type_Omap__pair_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
    produc1411910245le_alt: ( fun_li90789869le_alt * fun_li90789869le_alt ) > fun_Pr1186243091le_alt ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____effng,type,
    produc73018783t_bool: fun_fu1428047277t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____effng_516,type,
    produc542980935t_bool: fun_fu1038320557t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____effng_517,type,
    produc762033828i_bool: fun_fu305848843i_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____effng_518,type,
    produc327487325l_bool: fun_fu449017469l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____effng_519,type,
    produc802256322t_bool: fun_fu403564141t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____effng_520,type,
    produc2013750231t_bool: fun_fu585342577t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M,type,
    produc631952405t_bool: fun_fu1512088215t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_521,type,
    produc632580864l_bool: fun_fu966664249l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_522,type,
    produc1727510830l_bool: fun_fu396414613l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_523,type,
    produc999826263l_bool: fun_fu1902406423l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_524,type,
    produc47507185t_bool: fun_fu1647821467t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_525,type,
    produc2052829583le_alt: fun_fu736403735le_alt ).

tff(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    collec12892580le_alt: fun_Ar17477381t_bool > fun_Ar17477381t_bool ).

tff(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    collec1597001935e_indi: fun_Ar1809396326i_bool > fun_Ar1809396326i_bool ).

tff(sy_c_Set_OCollect_000tc__Nat__Onat,type,
    collect_nat: fun_nat_bool > fun_nat_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin,type,
    collec1236161569t_bool: fun_fu3835832l_bool > fun_fu3835832l_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
    collec71394895t_bool: fun_fu2098777574l_bool > fun_fu2098777574l_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effng,type,
    collec2125531966t_bool: fun_fu638310559l_bool > fun_fu638310559l_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
    collec1988958098le_alt: fun_Pr2067565481t_bool > fun_Pr2067565481t_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__Arrow____Order____Mirabelle____effngqiq,type,
    transi1687363644le_alt: fun_Pr2067565481t_bool > fun_Pr2067565481t_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__Arrow____Order____Mira,type,
    transi1124010071le_alt: fun_Pr486337689t_bool > fun_Pr486337689t_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__List__Olist_Itc__Arrow,type,
    transi1249888786le_alt: fun_Pr729410217t_bool > fun_Pr729410217t_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Arrow____Order____Mirabelle__,type,
    transi472504058le_alt: fun_Pr773225055t_bool > fun_Pr773225055t_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Arrow____Ord,type,
    transi434738282le_alt: fun_Pr31738815t_bool > fun_Pr31738815t_bool ).

tff(sy_c_fFalse,type,
    fFalse: bool ).

tff(sy_c_fNot,type,
    fNot: fun_bool_bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fconj,type,
    fconj: bool > fun_bool_bool ).

tff(sy_c_fequal_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    fequal1590852494le_alt: fun_Ar331856045t_bool ).

tff(sy_c_fequal_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    fequal1182599525e_indi: fun_Ar14145203i_bool ).

tff(sy_c_fequal_000tc__HOL__Obool,type,
    fequal_bool: fun_bo1549164019l_bool ).

tff(sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
    fequal928191109le_alt: fun_li495175091t_bool ).

tff(sy_c_fequal_000tc__Nat__Onat,type,
    fequal_nat: fun_nat_fun_nat_bool ).

tff(sy_c_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc,type,
    fequal957608631t_bool: fun_fu257364531l_bool ).

tff(sy_c_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    fequal1249241829t_bool: fun_fu1441209011l_bool ).

tff(sy_c_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    fequal1830749992t_bool: fun_fu643206625l_bool ).

tff(sy_c_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc,type,
    fequal346320936le_alt: fun_Pr330364403t_bool ).

tff(sy_c_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____eff,type,
    fequal1054218392le_alt: fun_Pr1025510259t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__HOL__Obo,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__List__Ol,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc_,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__526,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__527,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__528,type,
    hAPP_A1316408339l_bool: ( fun_Ar949229051l_bool * arrow_1893660431le_alt ) > fun_Ar1433468301l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__529,type,
    hAPP_A98481698t_bool: ( fun_Ar113775056t_bool * arrow_1893660431le_alt ) > fun_Ar249464360t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__530,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__531,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__532,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__533,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__534,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__535,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__536,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__537,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__538,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__539,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__540,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__541,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__542,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__543,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__544,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__545,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__546,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__547,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__548,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__prod_Itc,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__HOL__Ob,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_549,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_550,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_551,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_552,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_553,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_554,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_555,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_556,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_557,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_558,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_Itc_559,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__prod_It,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__prod_It_560,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____effng,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____effng_561,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____effng_562,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__prod_Itc__HOL__Obool,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__L,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_563,type,
    hAPP_b1029214724t_bool: ( fun_bo559790694t_bool * bool ) > fun_fu2114379172t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_,type,
    hAPP_b1787118453l_bool: ( fun_bo492988759l_bool * bool ) > fun_fu1255657237l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____,type,
    hAPP_b1777246598l_bool: ( fun_bo1445676730l_bool * bool ) > fun_fu2098777574l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___,type,
    hAPP_b1272691967l_bool: ( fun_bo377688929l_bool * bool ) > fun_fu638310559l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,type,
    hAPP_b128655177t_bool: ( fun_bo1431306493t_bool * bool ) > fun_Pr2067565481t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____effn,type,
    hAPP_b2094455111le_alt: ( fun_bo1682907689le_alt * bool ) > produc472769767le_alt ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_b2048821609l_bool: ( fun_bo41233099l_bool * bool ) > produc373466377l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal,type,
    hAPP_l499746980t_bool: ( fun_li1109619974t_bool * list_A114658244le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_564,type,
    hAPP_l84111627le_alt: ( fun_li90789869le_alt * list_A114658244le_alt ) > list_A114658244le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_565,type,
    hAPP_l1084348419lt_nat: ( fun_li1574574519lt_nat * list_A114658244le_alt ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_566,type,
    hAPP_l1822938419le_alt: ( fun_li164935701le_alt * list_A114658244le_alt ) > fun_Ar849108972le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_567,type,
    hAPP_l82091775t_bool: ( fun_li495175091t_bool * list_A114658244le_alt ) > fun_li1109619974t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_568,type,
    hAPP_l86320102le_alt: ( fun_li264309018le_alt * list_A114658244le_alt ) > fun_li90789869le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_569,type,
    hAPP_l362966444l_bool: ( fun_li1290371598l_bool * list_A114658244le_alt ) > fun_li1316747877l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_570,type,
    hAPP_l830471642l_bool: ( fun_li123689532l_bool * list_A114658244le_alt ) > fun_li2131491731l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_571,type,
    hAPP_l328381505l_bool: ( fun_li1959074549l_bool * list_A114658244le_alt ) > fun_li235657544l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_572,type,
    hAPP_l776557489l_bool: ( fun_li312794341l_bool * list_A114658244le_alt ) > fun_li143410744l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_573,type,
    hAPP_l1232500765t_bool: ( fun_li1684108543t_bool * list_A114658244le_alt ) > fun_li2098791382t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_574,type,
    hAPP_l1985992967le_alt: ( fun_li2074124649le_alt * list_A114658244le_alt ) > fun_li101108800le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_575,type,
    hAPP_l660415097le_alt: ( fun_li380014893le_alt * list_A114658244le_alt ) > fun_li47571840le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_576,type,
    hAPP_l1201992822le_alt: ( fun_li638184490le_alt * list_A114658244le_alt ) > fun_li397702653le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_577,type,
    hAPP_l1210406190le_alt: ( fun_li20309264le_alt * list_A114658244le_alt ) > fun_na86871399le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_578,type,
    hAPP_l1144124209l_bool: ( fun_li1316747877l_bool * list_A114658244le_alt ) > fun_fu3835832l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_579,type,
    hAPP_l1280938307l_bool: ( fun_li1194870181l_bool * list_A114658244le_alt ) > fun_fu741268092l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_580,type,
    hAPP_l1263040137le_alt: ( fun_li967808957le_alt * list_A114658244le_alt ) > fun_fu1561601296le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_581,type,
    hAPP_l384915638le_alt: ( fun_li1530812010le_alt * list_A114658244le_alt ) > fun_fu244651069le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_582,type,
    hAPP_l592144991l_bool: ( fun_li2131491731l_bool * list_A114658244le_alt ) > fun_fu2098777574l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_583,type,
    hAPP_l1876389606l_bool: ( fun_li235657544l_bool * list_A114658244le_alt ) > fun_fu638310559l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_584,type,
    hAPP_l515395158l_bool: ( fun_li143410744l_bool * list_A114658244le_alt ) > fun_fu669698703l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_585,type,
    hAPP_l706029667t_bool: ( fun_li359495831t_bool * list_A114658244le_alt ) > fun_fu72882922t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_586,type,
    hAPP_l1875392034t_bool: ( fun_li2098791382t_bool * list_A114658244le_alt ) > fun_Pr2067565481t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_587,type,
    hAPP_l859329548le_alt: ( fun_li101108800le_alt * list_A114658244le_alt ) > fun_Pr1186243091le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_588,type,
    hAPP_l1580775710le_alt: ( fun_li47571840le_alt * list_A114658244le_alt ) > produc587761367le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin,type,
    hAPP_l311606797i_bool: ( fun_li1640834235i_bool * list_A270647749e_indi ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin_589,type,
    hAPP_l713773333e_indi: ( fun_li651424637e_indi * list_A270647749e_indi ) > list_A270647749e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin_590,type,
    hAPP_l963769037e_indi: ( fun_li1386059829e_indi * list_A270647749e_indi ) > fun_li651424637e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin_591,type,
    hAPP_l814083573e_indi: ( fun_li1160816419e_indi * list_A270647749e_indi ) > fun_li675055941e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin_592,type,
    hAPP_l321397271e_indi: ( fun_li675055941e_indi * list_A270647749e_indi ) > produc2130070887e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__HOL__Obool,type,
    hAPP_list_bool_bool: ( fun_list_bool_bool * list_bool ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__List__Olist_Itc__HOL__Oboo,type,
    hAPP_l1189022293t_bool: ( fun_li107039421t_bool * list_bool ) > list_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__fun_Itc__List__Olist_Itc__,type,
    hAPP_l1947611924t_bool: ( fun_li662746748t_bool * list_bool ) > fun_li107039421t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__fun_Itc__List__Olist_Itc___593,type,
    hAPP_l218095399t_bool: ( fun_li998062677t_bool * list_bool ) > fun_li1455667518t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__prod_Itc__List__Olist_Itc_,type,
    hAPP_l1349316624t_bool: ( fun_li1455667518t_bool * list_bool ) > produc1754317479t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,
    hAPP_l527728301t_bool: ( fun_li449870427t_bool * list_l2028444773le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___594,type,
    hAPP_l1913469717le_alt: ( fun_li397702653le_alt * list_l2028444773le_alt ) > list_l2028444773le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___595,type,
    hAPP_l1496043450lt_nat: ( fun_li1064136482lt_nat * list_l2028444773le_alt ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___596,type,
    hAPP_l246742955t_bool: ( fun_li1489248217t_bool * list_l2028444773le_alt ) > fun_li449870427t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___597,type,
    hAPP_l2145422509le_alt: ( fun_li485644309le_alt * list_l2028444773le_alt ) > fun_li397702653le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___598,type,
    hAPP_l949242293le_alt: ( fun_li1998532451le_alt * list_l2028444773le_alt ) > fun_li1694444645le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___599,type,
    hAPP_l571271991le_alt: ( fun_li1694444645le_alt * list_l2028444773le_alt ) > produc1753437671le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__HOL__Obool,type,
    hAPP_list_nat_bool: ( fun_list_nat_bool * list_nat ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__List__Olist_Itc__Nat__Onat_,type,
    hAPP_l248265089st_nat: ( fun_li1155097699st_nat * list_nat ) > list_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__fun_Itc__List__Olist_Itc__N,type,
    hAPP_l710375585st_nat: ( fun_li511653589st_nat * list_nat ) > fun_li1155097699st_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__fun_Itc__List__Olist_Itc__N_600,type,
    hAPP_l1148138287st_nat: ( fun_li1596838627st_nat * list_nat ) > fun_li1832077297st_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__prod_Itc__List__Olist_Itc__,type,
    hAPP_l318352527st_nat: ( fun_li1832077297st_nat * list_nat ) > produc78950733st_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
    hAPP_l446901855l_bool: ( fun_li764922637l_bool * list_f1976315671t_bool ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq_601,type,
    hAPP_l179891349t_bool: ( fun_li1129981181t_bool * list_f1976315671t_bool ) > list_f1976315671t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq_602,type,
    hAPP_l352082555t_bool: ( fun_li482685923t_bool * list_f1976315671t_bool ) > fun_li1129981181t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq_603,type,
    hAPP_l197476889t_bool: ( fun_li831465799t_bool * list_f1976315671t_bool ) > fun_li311660567t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq_604,type,
    hAPP_l905633001t_bool: ( fun_li311660567t_bool * list_f1976315671t_bool ) > produc1771156199t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_,type,
    hAPP_l1502732685l_bool: ( fun_li1841738811l_bool * list_f1981087045t_bool ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__605,type,
    hAPP_l1936976149t_bool: ( fun_li1328417149t_bool * list_f1981087045t_bool ) > list_f1981087045t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__606,type,
    hAPP_l2140505421t_bool: ( fun_li1021842101t_bool * list_f1981087045t_bool ) > fun_li1328417149t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__607,type,
    hAPP_l559590133t_bool: ( fun_li1552454179t_bool * list_f1981087045t_bool ) > fun_li189252293t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__608,type,
    hAPP_l2146059159t_bool: ( fun_li189252293t_bool * list_f1981087045t_bool ) > produc446876519t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle,type,
    hAPP_l1252368702l_bool: ( fun_li2047702944l_bool * list_f733367646t_bool ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_609,type,
    hAPP_l1229506623t_bool: ( fun_li1539627809t_bool * list_f733367646t_bool ) > list_f733367646t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_610,type,
    hAPP_l1290257408t_bool: ( fun_li633046836t_bool * list_f733367646t_bool ) > fun_li1539627809t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_611,type,
    hAPP_l315980333t_bool: ( fun_li1459743457t_bool * list_f733367646t_bool ) > fun_li1817929038t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_612,type,
    hAPP_l1900989676t_bool: ( fun_li1817929038t_bool * list_f733367646t_bool ) > produc819494411t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____effng,type,
    hAPP_l423847376t_bool: ( fun_li2133552254t_bool * list_P1419683592le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____effng_613,type,
    hAPP_l1424955733le_alt: ( fun_li1098897981le_alt * list_P1419683592le_alt ) > list_P1419683592le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____effng_614,type,
    hAPP_l1433766794le_alt: ( fun_li1077448946le_alt * list_P1419683592le_alt ) > fun_li1098897981le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____effng_615,type,
    hAPP_l48758843le_alt: ( fun_li946730985le_alt * list_P1419683592le_alt ) > fun_li71228744le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____effng_616,type,
    hAPP_l1149277722le_alt: ( fun_li71228744le_alt * list_P1419683592le_alt ) > produc700249127le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M,type,
    hAPP_l255772864t_bool: ( fun_li154183278t_bool * list_P662130680le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_617,type,
    hAPP_l922056661le_alt: ( fun_li262510141le_alt * list_P662130680le_alt ) > list_P662130680le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_618,type,
    hAPP_l581970330le_alt: ( fun_li375927042le_alt * list_P662130680le_alt ) > fun_li262510141le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_619,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_620,type,
    hAPP_l235329034le_alt: ( fun_li1627626296le_alt * list_P662130680le_alt ) > produc1259311655le_alt ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,type,
    hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,
    hAPP_n2007559481le_alt: ( fun_na86871399le_alt * nat ) > list_A114658244le_alt ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Nat__Onat,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
    hAPP_n1622045025le_alt: ( fun_na1003310479le_alt * nat ) > fun_Ar849108972le_alt ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____effngq_621,type,
    hAPP_n2138229611t_bool: ( fun_na296811289t_bool * nat ) > fun_Ar274636406t_bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mi,type,
    hAPP_n372949560le_alt: ( fun_na960272160le_alt * nat ) > fun_li90789869le_alt ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mi_622,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__Li,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__Lis,type,
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    hAPP_P588680495t_bool: ( fun_Pr1701595235t_bool * produc472769767le_alt ) > fun_Pr486337689t_bool ).

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    hAPP_P2117677505le_alt: ( fun_Pr139923747le_alt * produc472769767le_alt ) > produc587761367le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___885,type,
    hAPP_P1322860167le_alt: ( fun_Pr1571129833le_alt * produc472769767le_alt ) > produc328685981le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_,type,
    hAPP_P67597801l_bool: ( fun_Pr148219083l_bool * produc7288727e_indi ) > fun_fu1362377551l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc_,type,
    hAPP_P738148045l_bool: ( fun_Pr292042671l_bool * produc373466377l_bool ) > fun_fu1710745281l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng,type,
    hAPP_P1894408759t_bool: ( fun_Pr486337689t_bool * produc587761367le_alt ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_886,type,
    hAPP_P94229072t_bool: ( fun_Pr908190898t_bool * produc587761367le_alt ) > fun_Ar274636406t_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_887,type,
    hAPP_P1680517091le_alt: ( fun_Pr1418635159le_alt * produc587761367le_alt ) > fun_li262510141le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_888,type,
    hAPP_P878768990l_bool: ( fun_Pr1204542610l_bool * produc587761367le_alt ) > fun_fu3835832l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_889,type,
    hAPP_P50207614t_bool: ( fun_Pr1188951520t_bool * produc587761367le_alt ) > fun_fu2114379172t_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_890,type,
    hAPP_P1986703244l_bool: ( fun_Pr1411261120l_bool * produc587761367le_alt ) > fun_fu2098777574l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_891,type,
    hAPP_P171164537l_bool: ( fun_Pr80661467l_bool * produc587761367le_alt ) > fun_fu638310559l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_892,type,
    hAPP_P489291369l_bool: ( fun_Pr2124911691l_bool * produc587761367le_alt ) > fun_fu669698703l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_893,type,
    hAPP_P1708597583t_bool: ( fun_Pr324456707t_bool * produc587761367le_alt ) > fun_Pr2067565481t_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_894,type,
    hAPP_P1907587391t_bool: ( fun_Pr1025510259t_bool * produc587761367le_alt ) > fun_Pr486337689t_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_895,type,
    hAPP_P1755135161le_alt: ( fun_Pr544315117le_alt * produc587761367le_alt ) > fun_Pr1186243091le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_896,type,
    hAPP_P1765681631le_alt: ( fun_Pr309696275le_alt * produc587761367le_alt ) > fun_Pr1876970297le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_897,type,
    hAPP_P211644097le_alt: ( fun_Pr1116498339le_alt * produc587761367le_alt ) > produc472769767le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_898,type,
    hAPP_P205052337le_alt: ( fun_Pr1186243091le_alt * produc587761367le_alt ) > produc587761367le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_899,type,
    hAPP_P740096983le_alt: ( fun_Pr1876970297le_alt * produc587761367le_alt ) > produc960031997le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____effng_900,type,
    hAPP_P329666697l_bool: ( fun_Pr1802290667l_bool * produc2130070887e_indi ) > fun_fu434159903l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Olist_Itc__H,type,
    hAPP_P1870454025l_bool: ( fun_Pr852727147l_bool * produc1754317479t_bool ) > fun_fu115111519l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____M,type,
    hAPP_P2060499849l_bool: ( fun_Pr222918635l_bool * produc1753437671le_alt ) > fun_fu1098893727l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__List__Olist_Itc__Na,type,
    hAPP_P1736545109l_bool: ( fun_Pr1920905527l_bool * produc78950733st_nat ) > fun_fu219123461l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle,type,
    hAPP_P1143334793l_bool: ( fun_Pr965291755l_bool * produc1771156199t_bool ) > fun_fu1636673183l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____,type,
    hAPP_P886531209l_bool: ( fun_Pr1568800235l_bool * produc446876519t_bool ) > fun_fu1317355295l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order___,type,
    hAPP_P563751121l_bool: ( fun_Pr1386485427l_bool * produc819494411t_bool ) > fun_fu576482755l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabell,type,
    hAPP_P641400329l_bool: ( fun_Pr1089205099l_bool * produc700249127le_alt ) > fun_fu316843999l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____,type,
    hAPP_P1538717705l_bool: ( fun_Pr2018445931l_bool * produc1259311655le_alt ) > fun_fu1235142111l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc__fun_Itc__p,type,
    hAPP_P1251024649l_bool: ( fun_Pr2045952363l_bool * product_prod_nat_nat ) > fun_fu56396127l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
    hAPP_P53043505l_bool: ( fun_Pr651137043l_bool * produc565898555t_bool ) > fun_fu1870245107l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn,type,
    hAPP_P1486810089l_bool: ( fun_Pr956743371l_bool * produc1998423703t_bool ) > fun_fu719424079l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff,type,
    hAPP_P1653001865l_bool: ( fun_Pr609214443l_bool * produc612505703t_bool ) > fun_fu1042517023l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    hAPP_P1862941685l_bool: ( fun_Pr158902231l_bool * produc328685981le_alt ) > fun_fu65955669l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
    hAPP_P1180049077l_bool: ( fun_Pr309360535l_bool * produc960031997le_alt ) > fun_fu1975327413l_bool ).

tff(sy_c_hBOOL,type,
    hBOOL: bool > $o ).

tff(sy_c_member_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt,type,
    member1502664802le_alt: fun_Ar569529141l_bool ).

tff(sy_c_member_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    member1479139729e_indi: fun_Ar1047186533l_bool ).

tff(sy_c_member_000tc__HOL__Obool,type,
    member_bool: fun_bo492988759l_bool ).

tff(sy_c_member_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
    member1145038001le_alt: fun_li1194870181l_bool ).

tff(sy_c_member_000tc__Nat__Onat,type,
    member_nat: fun_na1436237685l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_,type,
    member870521227t_bool: fun_fu2087919193l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__901,type,
    member346602425t_bool: fun_fu895753397l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__902,type,
    member144328170t_bool: fun_fu1058347573l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__903,type,
    member2099084668le_alt: fun_fu68111675l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc,type,
    member1124505298t_bool: fun_fu846523317l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_904,type,
    member785631232t_bool: fun_fu1072826421l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_905,type,
    member933336803t_bool: fun_fu361117961l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_906,type,
    member387840963le_alt: fun_fu2141985013l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____Mirabelle,type,
    member344984203t_bool: fun_fu302299893l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Order____,type,
    member1782492345t_bool: fun_fu1407717749l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____Order___,type,
    member1133581546t_bool: fun_fu827796887l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____Mirabell,type,
    member684813948le_alt: fun_fu662095797l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__fun_Itc__Arrow____Order____Mirabelle_,type,
    member1931034374t_bool: fun_fu1049365455l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__fun_Itc__fun_Itc__Arrow____Order____M,type,
    member1683162164t_bool: fun_fu434014251l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__fun_Itc__prod_Itc__Arrow____Order____,type,
    member883057071t_bool: fun_fu2051014645l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__prod_Itc__Arrow____Order____Mirabelle,type,
    member1393348599le_alt: fun_fu475251505l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    member472043127le_alt: fun_fu1840166961l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___907,type,
    member282602450e_indi: fun_fu1607936949l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___908,type,
    member1020280587l_bool: fun_fu2080348917l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___909,type,
    member1103199858ol_nat: fun_fu1865022631l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___910,type,
    member173038353t_bool: fun_fu1383920485l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___911,type,
    member555261573le_alt: fun_fu1337854581l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,type,
    member169834185le_alt: fun_fu496394965l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_912,type,
    member1247254528e_indi: fun_fu1843791925l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_913,type,
    member1173995577l_bool: fun_fu2017702261l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_914,type,
    member1799279044ol_nat: fun_fu1129139019l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_915,type,
    member599168435le_alt: fun_fu854556917l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,type,
    member786328118le_alt: fun_fu843395893l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_916,type,
    member1220706259e_indi: fun_fu687131369l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_917,type,
    member340585612l_bool: fun_fu1253304283l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_918,type,
    member725377201ol_nat: fun_fu1006935669l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_919,type,
    member149997830le_alt: fun_fu1367945935l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    member902318790le_alt: fun_fu1319253455l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__920,type,
    member1558233923e_indi: fun_fu916781301l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__921,type,
    member1069471740t_bool: fun_fu864675765l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__922,type,
    member1130928449lt_nat: fun_fu1988068037l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__923,type,
    member1449157750le_alt: fun_fu1703474229l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    member234726149t_bool: fun_fu1437756021l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_924,type,
    member1431564083t_bool: fun_fu1634738421l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_925,type,
    member1190141424t_bool: fun_fu760706467l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_926,type,
    member278248694le_alt: fun_fu1675678773l_bool ).

tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc,type,
    member1333168212le_alt: fun_Pr1085078251l_bool ).

tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mt,type,
    member155382916e_indi: fun_Pr148219083l_bool ).

tff(sy_c_member_000tc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    member624253174l_bool: fun_Pr292042671l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____eff,type,
    member1401409220le_alt: fun_Pr2124911691l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____eff_927,type,
    member1257664212e_indi: fun_Pr1802290667l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Olist_Itc_,type,
    member1058364180t_bool: fun_Pr852727147l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order___,type,
    member399934036le_alt: fun_Pr222918635l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__List__Olist_Itc__,type,
    member910422074st_nat: fun_Pr1920905527l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabel,type,
    member2134761044t_bool: fun_Pr965291755l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order__,type,
    member292487380t_bool: fun_Pr1568800235l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order_,type,
    member2002415608t_bool: fun_Pr1386485427l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabe,type,
    member828077460le_alt: fun_Pr1089205099l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow__,type,
    member2130615444le_alt: fun_Pr2018445931l_bool ).

tff(sy_c_member_000tc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J,type,
    member232255508at_nat: fun_Pr2045952363l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    member565818408t_bool: fun_Pr651137043l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ef,type,
    member331044740t_bool: fun_Pr956743371l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____e,type,
    member1681679828t_bool: fun_Pr609214443l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs,type,
    member916027018le_alt: fun_Pr158902231l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,
    member74519274le_alt: fun_Pr309360535l_bool ).

tff(sy_v_F,type,
    f: fun_fu2114379172t_bool ).

tff(sy_v_P_H____,type,
    p_1: fun_Ar274636406t_bool ).

tff(sy_v_P____,type,
    p: fun_Ar274636406t_bool ).

tff(sy_v_a____,type,
    a: arrow_1893660431le_alt ).

tff(sy_v_b____,type,
    b: arrow_1893660431le_alt ).

tff(sy_v_c____,type,
    c: arrow_1893660431le_alt ).

%----Relevant facts (1200)
tff(fact_0__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p),arrow_5070731e_Prof)) ).

tff(fact_1_assms_I3_J,axiom,
    hBOOL(hAPP_f1572141188l_bool(arrow_1335103695le_IIA,f)) ).

tff(fact_2_u,axiom,
    hBOOL(hAPP_f1572141188l_bool(arrow_320876018nimity,f)) ).

tff(fact_3__096a_A_126_061_Ab_096,axiom,
    a != b ).

tff(fact_4_dist,axiom,
    hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,a),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,b),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt))))) ).

tff(fact_5_iff,axiom,
    ! [I: arrow_856714788e_indi] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,I)))
    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),hAPP_A1646126530t_bool(p_1,I))) ) ).

tff(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_,axiom,
    ~ ! [C_5: arrow_1893660431le_alt] : ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,a),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,b),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,C_5),nil_Ar557011903le_alt))))) ).

tff(fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,arrow_1525312447_below),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,arrow_1525312447_below),p)),c)),b))),b)),a)),arrow_5070731e_Prof)) ).

tff(fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,arrow_1525312447_below),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,arrow_1525312447_below),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,arrow_1525312447_below),p)),c)),b))),b)),a))),a)),c)),arrow_5070731e_Prof)) ).

tff(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,arrow_1525312447_below),p)),c)),b)),arrow_5070731e_Prof)) ).

tff(fact_10_in__mkbot,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool,Z_3: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(arrow_1481558583_mkbot(L_2),Z_3)))
    <=> ( ( Y_2 != Z_3 )
        & ( ( X_2 = Z_3 )
         => ( X_2 != Y_2 ) )
        & ( ( X_2 != Z_3 )
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_2)) ) ) ) ).

tff(fact_11_in__mktop,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool,Z_3: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(arrow_1630265669_mktop(L_2),Z_3)))
    <=> ( ( X_2 != Z_3 )
        & ( ( Y_2 = Z_3 )
         => ( X_2 != Y_2 ) )
        & ( ( Y_2 != Z_3 )
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_2)) ) ) ) ).

tff(fact_12_in__below,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
       => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,L_2),Aa),Ba)))
        <=> ( ( X_2 != Y_2 )
            & ( ( Y_2 = Aa )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Ba)),L_2)) )
            & ( ( Y_2 != Aa )
             => ( ( ( X_2 = Aa )
                 => ( ( Y_2 = Ba )
                    | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Y_2)),L_2)) ) )
                & ( ( X_2 != Aa )
                 => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_2)) ) ) ) ) ) ) ) ).

tff(fact_13_split__paired__All,axiom,
    ! [Pa: fun_Pr486337689t_bool] :
      ( ! [X1: produc587761367le_alt] : hBOOL(hAPP_P1894408759t_bool(Pa,X1))
    <=> ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] : hBOOL(hAPP_P1894408759t_bool(Pa,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6))) ) ).

tff(fact_14_split__paired__All,axiom,
    ! [Pa: fun_Pr2067565481t_bool] :
      ( ! [X1: produc472769767le_alt] : hBOOL(hAPP_P1178790471t_bool(Pa,X1))
    <=> ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] : hBOOL(hAPP_P1178790471t_bool(Pa,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6))) ) ).

tff(fact_15_Pair__eq,axiom,
    ! [Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,A_8: list_A114658244le_alt,B_7: list_A114658244le_alt] :
      ( ( hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_8),B_7) )
    <=> ( ( Aa = A_8 )
        & ( Ba = B_7 ) ) ) ).

tff(fact_16_Pair__eq,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,A_8: arrow_1893660431le_alt,B_7: arrow_1893660431le_alt] :
      ( ( hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba) = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_8),B_7) )
    <=> ( ( Aa = A_8 )
        & ( Ba = B_7 ) ) ) ).

tff(fact_17_Pair__inject,axiom,
    ! [A_12: list_A114658244le_alt,B_9: list_A114658244le_alt,A_11: list_A114658244le_alt,B_8: list_A114658244le_alt] :
      ( ( hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_12),B_9) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_11),B_8) )
     => ~ ( ( A_12 = A_11 )
         => ( B_9 != B_8 ) ) ) ).

tff(fact_18_Pair__inject,axiom,
    ! [A_12: arrow_1893660431le_alt,B_9: arrow_1893660431le_alt,A_11: arrow_1893660431le_alt,B_8: arrow_1893660431le_alt] :
      ( ( hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_12),B_9) = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_11),B_8) )
     => ~ ( ( A_12 = A_11 )
         => ( B_9 != B_8 ) ) ) ).

tff(fact_19_in__rel__def,axiom,
    ! [R_1: fun_Pr486337689t_bool,X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(in_rel2123099320le_alt(R_1),X_2),Y_2))
    <=> hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_1)) ) ).

tff(fact_20_in__rel__def,axiom,
    ! [R_1: fun_Pr2067565481t_bool,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(in_rel1496001986le_alt(R_1),X_2),Y_2))
    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_1)) ) ).

tff(fact_21_below__Lin,axiom,
    ! [L_2: fun_Pr2067565481t_bool,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt] :
      ( ( X_2 != Y_2 )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,L_2),X_2),Y_2)),arrow_1361987423le_Lin)) ) ) ).

tff(fact_22__096P_H_A_058_AProf_096,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p_1),arrow_5070731e_Prof)) ).

tff(fact_23__C1_C,axiom,
    ! [P_a: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,A_8: arrow_1893660431le_alt,B_7: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( ( A_8 != B_7 )
       => ( ( Aa != B_7 )
         => ( ( Ba != A_8 )
           => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
             => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_a),arrow_5070731e_Prof))
               => ( ! [I: arrow_856714788e_indi] :
                      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I)))
                    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_8),B_7)),hAPP_A1646126530t_bool(P_a,I))) )
                 => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
                   => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_8),B_7)),hAPP_f2008608496t_bool(f,P_a))) ) ) ) ) ) ) ) ) ).

tff(fact_24__C2_C,axiom,
    ! [P_a: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,A_8: arrow_1893660431le_alt,B_7: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( ( A_8 != B_7 )
       => ( ( Aa != B_7 )
         => ( ( Ba != A_8 )
           => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
             => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_a),arrow_5070731e_Prof))
               => ( ! [I: arrow_856714788e_indi] :
                      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I)))
                    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_8),B_7)),hAPP_A1646126530t_bool(P_a,I))) )
                 => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
                  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_8),B_7)),hAPP_f2008608496t_bool(f,P_a))) ) ) ) ) ) ) ) ) ).

tff(fact_25_assms_I1_J,axiom,
    hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,f),pi_fun1746584570t_bool(arrow_5070731e_Prof,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,arrow_1361987423le_Lin)))) ).

tff(fact_26_const__Lin__Prof,axiom,
    ! [L_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_f480276746t_bool(cOMBK_1650320063e_indi,L_2)),arrow_5070731e_Prof)) ) ).

tff(fact_27_mkbot__Lin,axiom,
    ! [X_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(arrow_1481558583_mkbot(L_2),X_2)),arrow_1361987423le_Lin)) ) ).

tff(fact_28_mktop__Lin,axiom,
    ! [X_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(arrow_1630265669_mktop(L_2),X_2)),arrow_1361987423le_Lin)) ) ).

tff(fact_29_Lin__irrefl,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),L_2))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Aa)),L_2)) ) ) ).

tff(fact_30_notin__Lin__iff,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
     => ( ( X_2 != Y_2 )
       => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_2))
        <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_2),X_2)),L_2)) ) ) ) ).

tff(fact_31_third__alt,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt] :
      ( ( A != B )
     => ? [C_5: arrow_1893660431le_alt] : hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,B),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,C_5),nil_Ar557011903le_alt))))) ) ).

tff(fact_32_IIA__def,axiom,
    ! [Fa: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f1572141188l_bool(arrow_1335103695le_IIA,Fa))
    <=> ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
         => ! [Xa: fun_Ar274636406t_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Xa),arrow_5070731e_Prof))
             => ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
                  ( ! [I: arrow_856714788e_indi] :
                      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1646126530t_bool(X_1,I)))
                    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1646126530t_bool(Xa,I))) )
                 => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_f2008608496t_bool(Fa,X_1)))
                  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_f2008608496t_bool(Fa,Xa))) ) ) ) ) ) ).

tff(fact_33_unanimity__def,axiom,
    ! [Fa: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f1572141188l_bool(arrow_320876018nimity,Fa))
    <=> ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
         => ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
              ( ! [I: arrow_856714788e_indi] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1646126530t_bool(X_1,I)))
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_f2008608496t_bool(Fa,X_1))) ) ) ) ).

tff(fact_34_complete__Lin,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ? [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),arrow_1361987423le_Lin))
          & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),X_1)) ) ) ).

tff(fact_35_in__above,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_2: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
       => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(arrow_216713899_above(L_2,Aa),Ba)))
        <=> ( ( X_2 != Y_2 )
            & ( ( X_2 = Ba )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Y_2)),L_2)) )
            & ( ( X_2 != Ba )
             => ( ( ( Y_2 = Ba )
                 => ( ( X_2 = Aa )
                    | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Aa)),L_2)) ) )
                & ( ( Y_2 != Ba )
                 => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_2)) ) ) ) ) ) ) ) ).

tff(fact_36_distinct_Osimps_I1_J,axiom,
    hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,nil_Ar557011903le_alt)) ).

tff(fact_37_list_Osimps_I2_J,axiom,
    ! [A_10: arrow_1893660431le_alt,List_4: list_A114658244le_alt] : ( nil_Ar557011903le_alt != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A_10),List_4) ) ).

tff(fact_38_list_Osimps_I3_J,axiom,
    ! [A_9: arrow_1893660431le_alt,List_3: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A_9),List_3) != nil_Ar557011903le_alt ) ).

tff(fact_39_alt3,axiom,
    ? [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt,C_5: arrow_1893660431le_alt] : hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A_7),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,B_6),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,C_5),nil_Ar557011903le_alt))))) ).

tff(fact_40_linear__alt,axiom,
    ? [L_3: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin)) ).

tff(fact_41_dictator__def,axiom,
    ! [Fa: fun_fu2114379172t_bool,I_1: arrow_856714788e_indi] :
      ( hBOOL(hAPP_A997847300i_bool(hAPP_f399308031i_bool(arrow_1765888670ctator,Fa),I_1))
    <=> ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
         => ( hAPP_f2008608496t_bool(Fa,X_1) = hAPP_A1646126530t_bool(X_1,I_1) ) ) ) ).

tff(fact_42_list_Oinject,axiom,
    ! [Aa: arrow_1893660431le_alt,List: list_A114658244le_alt,A_8: arrow_1893660431le_alt,List_2: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Aa),List) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A_8),List_2) )
    <=> ( ( Aa = A_8 )
        & ( List = List_2 ) ) ) ).

tff(fact_43_not__Cons__self2,axiom,
    ! [X_39: arrow_1893660431le_alt,Xs_53: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_39),Xs_53) != Xs_53 ) ).

tff(fact_44_not__Cons__self,axiom,
    ! [Xs_52: list_A114658244le_alt,X_38: arrow_1893660431le_alt] : ( Xs_52 != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_38),Xs_52) ) ).

tff(fact_45_above__Lin,axiom,
    ! [L_2: fun_Pr2067565481t_bool,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt] :
      ( ( X_2 != Y_2 )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(arrow_216713899_above(L_2,X_2),Y_2)),arrow_1361987423le_Lin)) ) ) ).

tff(fact_46_dictatorI,axiom,
    ! [I_1: arrow_856714788e_indi,Fa: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Fa),pi_fun1746584570t_bool(arrow_5070731e_Prof,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,arrow_1361987423le_Lin))))
     => ( ! [X_1: fun_Ar274636406t_bool] :
            ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
           => ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
                ( ( A_7 != B_6 )
               => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1646126530t_bool(X_1,I_1)))
                 => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_f2008608496t_bool(Fa,X_1))) ) ) )
       => hBOOL(hAPP_A997847300i_bool(hAPP_f399308031i_bool(arrow_1765888670ctator,Fa),I_1)) ) ) ).

tff(fact_47_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr1780397033l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_2)),hAPP_P1103642805l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1)) ) ) ).

tff(fact_48_PiE,axiom,
    ! [X_2: nat,F: fun_na654729482le_alt,A_1: fun_nat_bool,B_1: fun_na998785244t_bool] :
      ( hBOOL(hAPP_f237532692l_bool(hAPP_f1907966927l_bool(member1393348599le_alt,F),pi_nat140973286le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_n216724700le_alt(F,X_2)),hAPP_n1161265524t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) ) ) ).

tff(fact_49_PiE,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr1116498339le_alt,A_1: fun_Pr486337689t_bool,B_1: fun_Pr324456707t_bool] :
      ( hBOOL(hAPP_f1446814201l_bool(hAPP_f141330253l_bool(member278248694le_alt,F),pi_Pro1151594295le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P211644097le_alt(F,X_2)),hAPP_P1708597583t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1)) ) ) ).

tff(fact_50_PiE,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar245737999le_alt,A_1: fun_Ar17477381t_bool,B_1: fun_Ar1573071255t_bool] :
      ( hBOOL(hAPP_f583850777l_bool(hAPP_f109138393l_bool(member2099084668le_alt,F),pi_Arr651462635le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(F,X_2)),hAPP_A1601437999t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1)) ) ) ).

tff(fact_51_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar338949104le_alt,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar274636406t_bool] :
      ( hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_2)),hAPP_A1646126530t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1)) ) ) ).

tff(fact_52_PiE,axiom,
    ! [X_2: bool,F: fun_bo1682907689le_alt,A_1: fun_bool_bool,B_1: fun_bo1431306493t_bool] :
      ( hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_2)),hAPP_b128655177t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) ) ) ).

tff(fact_53_PiE,axiom,
    ! [X_2: nat,F: fun_na296811289t_bool,A_1: fun_nat_bool,B_1: fun_na6909291l_bool] :
      ( hBOOL(hAPP_f1910182691l_bool(hAPP_f1251101421l_bool(member1931034374t_bool,F),pi_nat1489913205t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_n2138229611t_bool(F,X_2)),hAPP_n2125602947l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) ) ) ).

tff(fact_54_PiE,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr908190898t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_Pr1204542610l_bool] :
      ( hBOOL(hAPP_f715770888l_bool(hAPP_f1658660365l_bool(member234726149t_bool,F),pi_Pro606697670t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P94229072t_bool(F,X_2)),hAPP_P878768990l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1)) ) ) ).

tff(fact_55_PiE,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar1623257374t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_Ar59992358l_bool] :
      ( hBOOL(hAPP_f1709974824l_bool(hAPP_f2017976695l_bool(member870521227t_bool,F),pi_Arr220620154t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(F,X_2)),hAPP_A850178878l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1)) ) ) ).

tff(fact_56_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar624010239t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1998664965l_bool] :
      ( hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_2)),hAPP_A1411662545l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1)) ) ) ).

tff(fact_57_PiE,axiom,
    ! [X_2: bool,F: fun_bo1476023096t_bool,A_1: fun_bool_bool,B_1: fun_bo2107365004l_bool] :
      ( hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_2)),hAPP_b1078573912l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) ) ) ).

tff(fact_58_PiE,axiom,
    ! [X_2: nat,F: fun_na998785244t_bool,A_1: fun_nat_bool,B_1: fun_na144630978l_bool] :
      ( hBOOL(hAPP_f2035897138l_bool(hAPP_f826277901l_bool(member883057071t_bool,F),pi_nat1942897898t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_n1161265524t_bool(F,X_2)),hAPP_n1134275860l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) ) ) ).

tff(fact_59_PiE,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr324456707t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_Pr80661467l_bool] :
      ( hBOOL(hAPP_f573096205l_bool(hAPP_f2100194497l_bool(member1190141424t_bool,F),pi_Pro469835097t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1708597583t_bool(F,X_2)),hAPP_P171164537l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1)) ) ) ).

tff(fact_60_PiE,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar1573071255t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_Ar339057223l_bool] :
      ( hBOOL(hAPP_f1590435821l_bool(hAPP_f467104333l_bool(member144328170t_bool,F),pi_Arr192316325t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(F,X_2)),hAPP_A442239897l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1)) ) ) ).

tff(fact_61_PiE,axiom,
    ! [X_2: bool,F: fun_bo1431306493t_bool,A_1: fun_bool_bool,B_1: fun_bo377688929l_bool] :
      ( hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_2)),hAPP_b1272691967l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) ) ) ).

tff(fact_62_PiE,axiom,
    ! [X_2: nat,F: fun_na2092219207t_bool,A_1: fun_nat_bool,B_1: fun_na138495129l_bool] :
      ( hBOOL(hAPP_f562872145l_bool(hAPP_f517158217l_bool(member1683162164t_bool,F),pi_nat608045987t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_n2091767705t_bool(F,X_2)),hAPP_n1555388849l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) ) ) ).

tff(fact_63_PiE,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr1188951520t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_Pr1411261120l_bool] :
      ( hBOOL(hAPP_f1470281014l_bool(hAPP_f666236045l_bool(member1431564083t_bool,F),pi_Pro87132148t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P50207614t_bool(F,X_2)),hAPP_P1986703244l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1)) ) ) ).

tff(fact_64_PiE,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar248516172t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_Ar1071883092l_bool] :
      ( hBOOL(hAPP_f585444950l_bool(hAPP_f868830675l_bool(member346602425t_bool,F),pi_Arr494635176t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1610503070t_bool(F,X_2)),hAPP_A1569148780l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1)) ) ) ).

tff(fact_65_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar286530093t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1321653811l_bool] :
      ( hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_2)),hAPP_A2084592127l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1)) ) ) ).

tff(fact_66_PiE,axiom,
    ! [X_2: bool,F: fun_bo559790694t_bool,A_1: fun_bool_bool,B_1: fun_bo1445676730l_bool] :
      ( hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_2)),hAPP_b1777246598l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) ) ) ).

tff(fact_67_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr392309332lt_nat,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr428964044t_bool] :
      ( hBOOL(hAPP_f69887326l_bool(hAPP_f1736181859l_bool(member1130928449lt_nat,F),pi_Pro847445418lt_nat(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P923196832lt_nat(F,X_2)),hAPP_P1123315306t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1)) ) ) ).

tff(fact_68_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr139923747le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr1701595235t_bool] :
      ( hBOOL(hAPP_f963889529l_bool(hAPP_f1110468429l_bool(member1449157750le_alt,F),pi_Pro910144055le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_P2117677505le_alt(F,X_2)),hAPP_P588680495t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1)) ) ) ).

tff(fact_69_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1196455769le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr1407669585t_bool] :
      ( hBOOL(hAPP_f125423203l_bool(hAPP_f434978669l_bool(member902318790le_alt,F),pi_Pro262333359le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_P909886117le_alt(F,X_2)),hAPP_P1328248815t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1)) ) ) ).

tff(fact_70_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1509342064e_indi,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr895221296i_bool] :
      ( hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_2)),hAPP_P1859429372i_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1)) ) ) ).

tff(fact_71_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1616460421ol_nat,A_1: fun_fu3835832l_bool,B_1: fun_fu1077134171t_bool] :
      ( hBOOL(hAPP_f462751375l_bool(hAPP_f1774924229l_bool(member1103199858ol_nat,F),pi_fun614388187ol_nat(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1262704593ol_nat(F,X_2)),hAPP_f595382009t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1)) ) ) ).

tff(fact_72_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1228726322le_alt,A_1: fun_fu3835832l_bool,B_1: fun_fu1258557076t_bool] :
      ( hBOOL(hAPP_f1673349000l_bool(hAPP_f1710130701l_bool(member555261573le_alt,F),pi_fun645774662le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f133306064le_alt(F,X_2)),hAPP_f1745861984t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1)) ) ) ).

tff(fact_73_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1224779274le_alt,A_1: fun_fu3835832l_bool,B_1: fun_fu2143707488t_bool] :
      ( hBOOL(hAPP_f1789660692l_bool(hAPP_f650195279l_bool(member472043127le_alt,F),pi_fun1760679520le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f1965185878le_alt(F,X_2)),hAPP_f1841273342t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1)) ) ) ).

tff(fact_74_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1929591039e_indi,A_1: fun_fu3835832l_bool,B_1: fun_fu223278561i_bool] :
      ( hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_2)),hAPP_f391644589i_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1)) ) ) ).

tff(fact_75_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu916327706l_bool] :
      ( hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_2)),hAPP_f1676084198l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1)) ) ) ).

tff(fact_76_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu841105374ol_nat,A_1: fun_fu638310559l_bool,B_1: fun_fu477456066t_bool] :
      ( hBOOL(hAPP_f461570100l_bool(hAPP_f1175388045l_bool(member725377201ol_nat,F),pi_fun476373740ol_nat(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1842225014ol_nat(F,X_2)),hAPP_f703394068t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1)) ) ) ).

tff(fact_77_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu1431796761le_alt,A_1: fun_fu638310559l_bool,B_1: fun_fu1924348397t_bool] :
      ( hBOOL(hAPP_f288351779l_bool(hAPP_f1909282029l_bool(member149997830le_alt,F),pi_fun34562933le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f1273325419le_alt(F,X_2)),hAPP_f369701637t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1)) ) ) ).

tff(fact_78_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu67587555le_alt,A_1: fun_fu638310559l_bool,B_1: fun_fu1534804551t_bool] :
      ( hBOOL(hAPP_f730470457l_bool(hAPP_f1494675789l_bool(member786328118le_alt,F),pi_fun1511699953le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f773337979le_alt(F,X_2)),hAPP_f234621849t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1)) ) ) ).

tff(fact_79_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu562005862e_indi,A_1: fun_fu638310559l_bool,B_1: fun_fu2142850746i_bool] :
      ( hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_2)),hAPP_f2010315474i_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1)) ) ) ).

tff(fact_80_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,A_1: fun_fu638310559l_bool,B_1: fun_fu237781875l_bool] :
      ( hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_2)),hAPP_f463104139l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1)) ) ) ).

tff(fact_81_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu60852439ol_nat,A_1: fun_fu2098777574l_bool,B_1: fun_fu1667513993t_bool] :
      ( hBOOL(hAPP_f1661238497l_bool(hAPP_f996655209l_bool(member1799279044ol_nat,F),pi_fun1997317165ol_nat(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1333555235ol_nat(F,X_2)),hAPP_f1550778407t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1)) ) ) ).

tff(fact_82_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu356555872le_alt,A_1: fun_fu2098777574l_bool,B_1: fun_fu2050451686t_bool] :
      ( hBOOL(hAPP_f2015026102l_bool(hAPP_f1071682701l_bool(member599168435le_alt,F),pi_fun294122868le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f257198334le_alt(F,X_2)),hAPP_f210821554t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1)) ) ) ).

tff(fact_83_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu71747932le_alt,A_1: fun_fu2098777574l_bool,B_1: fun_fu1566951310t_bool] :
      ( hBOOL(hAPP_f975067494l_bool(hAPP_f1946164211l_bool(member169834185le_alt,F),pi_fun1429765554le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f398149800le_alt(F,X_2)),hAPP_f2038412844t_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1)) ) ) ).

tff(fact_84_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu748153389e_indi,A_1: fun_fu2098777574l_bool,B_1: fun_fu2109152051i_bool] :
      ( hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_2)),hAPP_f399308031i_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1)) ) ) ).

tff(fact_85_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,A_1: fun_fu2098777574l_bool,B_1: fun_fu1522163052l_bool] :
      ( hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_2)),hAPP_f414129720l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1)) ) ) ).

tff(fact_86_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu2114379172t_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu1863781882l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_2)),hAPP_f1915815064l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1)) ) ) ).

tff(fact_87_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar274636406t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1474557608l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_2)),hAPP_A897398598l_bool(B_1,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1)) ) ) ).

tff(fact_88_list_Oexhaust,axiom,
    ! [Y_15: list_A114658244le_alt] :
      ( ( Y_15 != nil_Ar557011903le_alt )
     => ~ ! [A_7: arrow_1893660431le_alt,List_1: list_A114658244le_alt] : ( Y_15 != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A_7),List_1) ) ) ).

tff(fact_89_neq__Nil__conv,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( Xs_1 != nil_Ar557011903le_alt )
    <=> ? [Y_9: arrow_1893660431le_alt,Ys: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Ys) ) ) ).

tff(fact_90_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,A_1: fun_Pr2067565481t_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,hAPP_f699791347l_bool(cOMBK_138598520le_alt,B_1))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_91_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr392309332lt_nat,A_1: fun_Pr2067565481t_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f69887326l_bool(hAPP_f1736181859l_bool(member1130928449lt_nat,F),pi_Pro847445418lt_nat(A_1,hAPP_f795770633t_bool(cOMBK_1524165667le_alt,B_1))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P923196832lt_nat(F,X_2)),B_1)) ) ) ).

tff(fact_92_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr139923747le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f963889529l_bool(hAPP_f1110468429l_bool(member1449157750le_alt,F),pi_Pro910144055le_alt(A_1,hAPP_f480827367t_bool(cOMBK_605104626le_alt,B_1))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_P2117677505le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_93_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1196455769le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f125423203l_bool(hAPP_f434978669l_bool(member902318790le_alt,F),pi_Pro262333359le_alt(A_1,hAPP_f1074682185t_bool(cOMBK_385683240le_alt,B_1))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_P909886117le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_94_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1509342064e_indi,A_1: fun_Pr2067565481t_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A_1,hAPP_f359069313i_bool(cOMBK_1987648063le_alt,B_1))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_2)),B_1)) ) ) ).

tff(fact_95_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1616460421ol_nat,A_1: fun_fu3835832l_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f462751375l_bool(hAPP_f1774924229l_bool(member1103199858ol_nat,F),pi_fun614388187ol_nat(A_1,hAPP_f1195142808t_bool(cOMBK_155500978t_bool,B_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1262704593ol_nat(F,X_2)),B_1)) ) ) ).

tff(fact_96_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1228726322le_alt,A_1: fun_fu3835832l_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f1673349000l_bool(hAPP_f1710130701l_bool(member555261573le_alt,F),pi_fun645774662le_alt(A_1,hAPP_f2020753944t_bool(cOMBK_342345345t_bool,B_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f133306064le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_97_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1224779274le_alt,A_1: fun_fu3835832l_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f1789660692l_bool(hAPP_f650195279l_bool(member472043127le_alt,F),pi_fun1760679520le_alt(A_1,hAPP_f1027939672t_bool(cOMBK_1334022583t_bool,B_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f1965185878le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_98_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1929591039e_indi,A_1: fun_fu3835832l_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A_1,hAPP_f2022065970i_bool(cOMBK_818801614t_bool,B_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_2)),B_1)) ) ) ).

tff(fact_99_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,A_1: fun_fu3835832l_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A_1,hAPP_f1582869284l_bool(cOMBK_542452487t_bool,B_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_2)),B_1)) ) ) ).

tff(fact_100_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu841105374ol_nat,A_1: fun_fu638310559l_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f461570100l_bool(hAPP_f1175388045l_bool(member725377201ol_nat,F),pi_fun476373740ol_nat(A_1,hAPP_f779832389t_bool(cOMBK_198318445t_bool,B_1))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1842225014ol_nat(F,X_2)),B_1)) ) ) ).

tff(fact_101_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu1431796761le_alt,A_1: fun_fu638310559l_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f288351779l_bool(hAPP_f1909282029l_bool(member149997830le_alt,F),pi_fun34562933le_alt(A_1,hAPP_f1369154921t_bool(cOMBK_1697579230t_bool,B_1))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f1273325419le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_102_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu67587555le_alt,A_1: fun_fu638310559l_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f730470457l_bool(hAPP_f1494675789l_bool(member786328118le_alt,F),pi_fun1511699953le_alt(A_1,hAPP_f1227262031t_bool(cOMBK_837265448t_bool,B_1))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f773337979le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_103_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu562005862e_indi,A_1: fun_fu638310559l_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A_1,hAPP_f1128827177i_bool(cOMBK_814147665t_bool,B_1))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_2)),B_1)) ) ) ).

tff(fact_104_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,A_1: fun_fu638310559l_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A_1,hAPP_f1713038057l_bool(cOMBK_118864600t_bool,B_1))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_2)),B_1)) ) ) ).

tff(fact_105_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu60852439ol_nat,A_1: fun_fu2098777574l_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f1661238497l_bool(hAPP_f996655209l_bool(member1799279044ol_nat,F),pi_fun1997317165ol_nat(A_1,hAPP_f1319616198t_bool(cOMBK_2008571104t_bool,B_1))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1333555235ol_nat(F,X_2)),B_1)) ) ) ).

tff(fact_106_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu356555872le_alt,A_1: fun_fu2098777574l_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f2015026102l_bool(hAPP_f1071682701l_bool(member599168435le_alt,F),pi_fun294122868le_alt(A_1,hAPP_f2065367146t_bool(cOMBK_1118451887t_bool,B_1))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f257198334le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_107_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu71747932le_alt,A_1: fun_fu2098777574l_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f975067494l_bool(hAPP_f1946164211l_bool(member169834185le_alt,F),pi_fun1429765554le_alt(A_1,hAPP_f1552202630t_bool(cOMBK_1544325605t_bool,B_1))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f398149800le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_108_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu748153389e_indi,A_1: fun_fu2098777574l_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A_1,hAPP_f448050564i_bool(cOMBK_443335420t_bool,B_1))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_2)),B_1)) ) ) ).

tff(fact_109_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,A_1: fun_fu2098777574l_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A_1,hAPP_f1152234870l_bool(cOMBK_1770320693t_bool,B_1))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_2)),B_1)) ) ) ).

tff(fact_110_funcset__mem,axiom,
    ! [X_2: nat,F: fun_na654729482le_alt,A_1: fun_nat_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f237532692l_bool(hAPP_f1907966927l_bool(member1393348599le_alt,F),pi_nat140973286le_alt(A_1,hAPP_f1409698632t_bool(cOMBK_1882555695ol_nat,B_1))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_n216724700le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_111_funcset__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr1116498339le_alt,A_1: fun_Pr486337689t_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f1446814201l_bool(hAPP_f141330253l_bool(member278248694le_alt,F),pi_Pro1151594295le_alt(A_1,hAPP_f1290118551t_bool(cOMBK_1555225330le_alt,B_1))))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P211644097le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_112_funcset__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar245737999le_alt,A_1: fun_Ar17477381t_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f583850777l_bool(hAPP_f109138393l_bool(member2099084668le_alt,F),pi_Arr651462635le_alt(A_1,hAPP_f1761571331t_bool(cOMBK_392407988le_alt,B_1))))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_113_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar338949104le_alt,A_1: fun_Ar1809396326i_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A_1,hAPP_f480276746t_bool(cOMBK_1650320063e_indi,B_1))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_114_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo1682907689le_alt,A_1: fun_bool_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A_1,hAPP_f1723896209t_bool(cOMBK_5056120l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_2)),B_1)) ) ) ).

tff(fact_115_funcset__mem,axiom,
    ! [X_2: nat,F: fun_na296811289t_bool,A_1: fun_nat_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f1910182691l_bool(hAPP_f1251101421l_bool(member1931034374t_bool,F),pi_nat1489913205t_bool(A_1,hAPP_f784815496l_bool(cOMBK_238368224ol_nat,B_1))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_n2138229611t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_116_funcset__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr908190898t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f715770888l_bool(hAPP_f1658660365l_bool(member234726149t_bool,F),pi_Pro606697670t_bool(A_1,hAPP_f1465094837l_bool(cOMBK_448375169le_alt,B_1))))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P94229072t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_117_funcset__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar1623257374t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f1709974824l_bool(hAPP_f2017976695l_bool(member870521227t_bool,F),pi_Arr220620154t_bool(A_1,hAPP_f1173384643l_bool(cOMBK_757054181le_alt,B_1))))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_118_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar624010239t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A_1,hAPP_f1352816552l_bool(cOMBK_1255579598e_indi,B_1))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_119_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo1476023096t_bool,A_1: fun_bool_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A_1,hAPP_f1322579375l_bool(cOMBK_317366791l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_120_funcset__mem,axiom,
    ! [X_2: nat,F: fun_na998785244t_bool,A_1: fun_nat_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f2035897138l_bool(hAPP_f826277901l_bool(member883057071t_bool,F),pi_nat1942897898t_bool(A_1,hAPP_f1191475300l_bool(cOMBK_214082799ol_nat,B_1))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_n1161265524t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_121_funcset__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr324456707t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f573096205l_bool(hAPP_f2100194497l_bool(member1190141424t_bool,F),pi_Pro469835097t_bool(A_1,hAPP_f908691129l_bool(cOMBK_1807543090le_alt,B_1))))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1708597583t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_122_funcset__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar1573071255t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f1590435821l_bool(hAPP_f467104333l_bool(member144328170t_bool,F),pi_Arr192316325t_bool(A_1,hAPP_f1301449449l_bool(cOMBK_935799668le_alt,B_1))))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_123_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo1431306493t_bool,A_1: fun_bool_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A_1,hAPP_f86272063l_bool(cOMBK_650639032l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_124_funcset__mem,axiom,
    ! [X_2: nat,F: fun_na2092219207t_bool,A_1: fun_nat_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f562872145l_bool(hAPP_f517158217l_bool(member1683162164t_bool,F),pi_nat608045987t_bool(A_1,hAPP_f1268543752l_bool(cOMBK_1485688882ol_nat,B_1))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_n2091767705t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_125_funcset__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr1188951520t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f1470281014l_bool(hAPP_f666236045l_bool(member1431564083t_bool,F),pi_Pro87132148t_bool(A_1,hAPP_f852696849l_bool(cOMBK_1524832687le_alt,B_1))))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P50207614t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_126_funcset__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar248516172t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f585444950l_bool(hAPP_f868830675l_bool(member346602425t_bool,F),pi_Arr494635176t_bool(A_1,hAPP_f1933295939l_bool(cOMBK_1583688247le_alt,B_1))))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1610503070t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_127_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar286530093t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A_1,hAPP_f258290692l_bool(cOMBK_1514079484e_indi,B_1))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_128_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo559790694t_bool,A_1: fun_bool_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A_1,hAPP_f369767947l_bool(cOMBK_2030738485l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_129_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu2114379172t_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,B_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_130_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar274636406t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,B_1))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_2)),B_1)) ) ) ).

tff(fact_131_splice_Osimps_I2_J,axiom,
    ! [V_2: arrow_1893660431le_alt,Va: list_A114658244le_alt] : ( hAPP_l84111627le_alt(splice791716242le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,V_2),Va)),nil_Ar557011903le_alt) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,V_2),Va) ) ).

tff(fact_132_list_Osimps_I4_J,axiom,
    ! [F1: list_A114658244le_alt,F2: fun_Ar1448189019le_alt] : ( hAPP_l84111627le_alt(list_c1024366775le_alt(F1,F2),nil_Ar557011903le_alt) = F1 ) ).

tff(fact_133_list_Osimps_I5_J,axiom,
    ! [F1: list_A114658244le_alt,F2: fun_Ar1448189019le_alt,Aa: arrow_1893660431le_alt,List: list_A114658244le_alt] : ( hAPP_l84111627le_alt(list_c1024366775le_alt(F1,F2),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Aa),List)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(F2,Aa),List) ) ).

tff(fact_134_split__paired__Ex,axiom,
    ! [Pa: fun_Pr486337689t_bool] :
      ( ? [X1: produc587761367le_alt] : hBOOL(hAPP_P1894408759t_bool(Pa,X1))
    <=> ? [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] : hBOOL(hAPP_P1894408759t_bool(Pa,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6))) ) ).

tff(fact_135_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2067565481t_bool] :
      ( ? [X1: produc472769767le_alt] : hBOOL(hAPP_P1178790471t_bool(Pa,X1))
    <=> ? [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] : hBOOL(hAPP_P1178790471t_bool(Pa,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6))) ) ).

tff(fact_136_splice_Osimps_I3_J,axiom,
    ! [X_37: arrow_1893660431le_alt,Xs_51: list_A114658244le_alt,Y_14: arrow_1893660431le_alt,Ys_20: list_A114658244le_alt] : ( hAPP_l84111627le_alt(splice791716242le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_37),Xs_51)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_14),Ys_20)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_37),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_14),hAPP_l84111627le_alt(splice791716242le_alt(Xs_51),Ys_20))) ) ).

tff(fact_137_splice_Osimps_I1_J,axiom,
    ! [Ys_19: list_A114658244le_alt] : ( hAPP_l84111627le_alt(splice791716242le_alt(nil_Ar557011903le_alt),Ys_19) = Ys_19 ) ).

tff(fact_138_splice__Nil2,axiom,
    ! [Xs_50: list_A114658244le_alt] : ( hAPP_l84111627le_alt(splice791716242le_alt(Xs_50),nil_Ar557011903le_alt) = Xs_50 ) ).

tff(fact_139_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr1780397033l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_2)),hAPP_P1103642805l_bool(B_1,X_2))) ) ) ).

tff(fact_140_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr392309332lt_nat,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr428964044t_bool] :
      ( hBOOL(hAPP_f69887326l_bool(hAPP_f1736181859l_bool(member1130928449lt_nat,F),pi_Pro847445418lt_nat(A_1,B_1)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P923196832lt_nat(F,X_2)),hAPP_P1123315306t_bool(B_1,X_2))) ) ) ).

tff(fact_141_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr139923747le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr1701595235t_bool] :
      ( hBOOL(hAPP_f963889529l_bool(hAPP_f1110468429l_bool(member1449157750le_alt,F),pi_Pro910144055le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_P2117677505le_alt(F,X_2)),hAPP_P588680495t_bool(B_1,X_2))) ) ) ).

tff(fact_142_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1196455769le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr1407669585t_bool] :
      ( hBOOL(hAPP_f125423203l_bool(hAPP_f434978669l_bool(member902318790le_alt,F),pi_Pro262333359le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_P909886117le_alt(F,X_2)),hAPP_P1328248815t_bool(B_1,X_2))) ) ) ).

tff(fact_143_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1509342064e_indi,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr895221296i_bool] :
      ( hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_2)),hAPP_P1859429372i_bool(B_1,X_2))) ) ) ).

tff(fact_144_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1616460421ol_nat,A_1: fun_fu3835832l_bool,B_1: fun_fu1077134171t_bool] :
      ( hBOOL(hAPP_f462751375l_bool(hAPP_f1774924229l_bool(member1103199858ol_nat,F),pi_fun614388187ol_nat(A_1,B_1)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1262704593ol_nat(F,X_2)),hAPP_f595382009t_bool(B_1,X_2))) ) ) ).

tff(fact_145_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1228726322le_alt,A_1: fun_fu3835832l_bool,B_1: fun_fu1258557076t_bool] :
      ( hBOOL(hAPP_f1673349000l_bool(hAPP_f1710130701l_bool(member555261573le_alt,F),pi_fun645774662le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f133306064le_alt(F,X_2)),hAPP_f1745861984t_bool(B_1,X_2))) ) ) ).

tff(fact_146_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1224779274le_alt,A_1: fun_fu3835832l_bool,B_1: fun_fu2143707488t_bool] :
      ( hBOOL(hAPP_f1789660692l_bool(hAPP_f650195279l_bool(member472043127le_alt,F),pi_fun1760679520le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f1965185878le_alt(F,X_2)),hAPP_f1841273342t_bool(B_1,X_2))) ) ) ).

tff(fact_147_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1929591039e_indi,A_1: fun_fu3835832l_bool,B_1: fun_fu223278561i_bool] :
      ( hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_2)),hAPP_f391644589i_bool(B_1,X_2))) ) ) ).

tff(fact_148_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu916327706l_bool] :
      ( hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_2)),hAPP_f1676084198l_bool(B_1,X_2))) ) ) ).

tff(fact_149_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu841105374ol_nat,A_1: fun_fu638310559l_bool,B_1: fun_fu477456066t_bool] :
      ( hBOOL(hAPP_f461570100l_bool(hAPP_f1175388045l_bool(member725377201ol_nat,F),pi_fun476373740ol_nat(A_1,B_1)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1842225014ol_nat(F,X_2)),hAPP_f703394068t_bool(B_1,X_2))) ) ) ).

tff(fact_150_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu1431796761le_alt,A_1: fun_fu638310559l_bool,B_1: fun_fu1924348397t_bool] :
      ( hBOOL(hAPP_f288351779l_bool(hAPP_f1909282029l_bool(member149997830le_alt,F),pi_fun34562933le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f1273325419le_alt(F,X_2)),hAPP_f369701637t_bool(B_1,X_2))) ) ) ).

tff(fact_151_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu67587555le_alt,A_1: fun_fu638310559l_bool,B_1: fun_fu1534804551t_bool] :
      ( hBOOL(hAPP_f730470457l_bool(hAPP_f1494675789l_bool(member786328118le_alt,F),pi_fun1511699953le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f773337979le_alt(F,X_2)),hAPP_f234621849t_bool(B_1,X_2))) ) ) ).

tff(fact_152_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu562005862e_indi,A_1: fun_fu638310559l_bool,B_1: fun_fu2142850746i_bool] :
      ( hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_2)),hAPP_f2010315474i_bool(B_1,X_2))) ) ) ).

tff(fact_153_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,A_1: fun_fu638310559l_bool,B_1: fun_fu237781875l_bool] :
      ( hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_2)),hAPP_f463104139l_bool(B_1,X_2))) ) ) ).

tff(fact_154_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu60852439ol_nat,A_1: fun_fu2098777574l_bool,B_1: fun_fu1667513993t_bool] :
      ( hBOOL(hAPP_f1661238497l_bool(hAPP_f996655209l_bool(member1799279044ol_nat,F),pi_fun1997317165ol_nat(A_1,B_1)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1333555235ol_nat(F,X_2)),hAPP_f1550778407t_bool(B_1,X_2))) ) ) ).

tff(fact_155_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu356555872le_alt,A_1: fun_fu2098777574l_bool,B_1: fun_fu2050451686t_bool] :
      ( hBOOL(hAPP_f2015026102l_bool(hAPP_f1071682701l_bool(member599168435le_alt,F),pi_fun294122868le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f257198334le_alt(F,X_2)),hAPP_f210821554t_bool(B_1,X_2))) ) ) ).

tff(fact_156_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu71747932le_alt,A_1: fun_fu2098777574l_bool,B_1: fun_fu1566951310t_bool] :
      ( hBOOL(hAPP_f975067494l_bool(hAPP_f1946164211l_bool(member169834185le_alt,F),pi_fun1429765554le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f398149800le_alt(F,X_2)),hAPP_f2038412844t_bool(B_1,X_2))) ) ) ).

tff(fact_157_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu748153389e_indi,A_1: fun_fu2098777574l_bool,B_1: fun_fu2109152051i_bool] :
      ( hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_2)),hAPP_f399308031i_bool(B_1,X_2))) ) ) ).

tff(fact_158_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,A_1: fun_fu2098777574l_bool,B_1: fun_fu1522163052l_bool] :
      ( hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_2)),hAPP_f414129720l_bool(B_1,X_2))) ) ) ).

tff(fact_159_Pi__mem,axiom,
    ! [X_2: nat,F: fun_na654729482le_alt,A_1: fun_nat_bool,B_1: fun_na998785244t_bool] :
      ( hBOOL(hAPP_f237532692l_bool(hAPP_f1907966927l_bool(member1393348599le_alt,F),pi_nat140973286le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_n216724700le_alt(F,X_2)),hAPP_n1161265524t_bool(B_1,X_2))) ) ) ).

tff(fact_160_Pi__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr1116498339le_alt,A_1: fun_Pr486337689t_bool,B_1: fun_Pr324456707t_bool] :
      ( hBOOL(hAPP_f1446814201l_bool(hAPP_f141330253l_bool(member278248694le_alt,F),pi_Pro1151594295le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P211644097le_alt(F,X_2)),hAPP_P1708597583t_bool(B_1,X_2))) ) ) ).

tff(fact_161_Pi__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar245737999le_alt,A_1: fun_Ar17477381t_bool,B_1: fun_Ar1573071255t_bool] :
      ( hBOOL(hAPP_f583850777l_bool(hAPP_f109138393l_bool(member2099084668le_alt,F),pi_Arr651462635le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(F,X_2)),hAPP_A1601437999t_bool(B_1,X_2))) ) ) ).

tff(fact_162_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar338949104le_alt,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar274636406t_bool] :
      ( hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_2)),hAPP_A1646126530t_bool(B_1,X_2))) ) ) ).

tff(fact_163_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo1682907689le_alt,A_1: fun_bool_bool,B_1: fun_bo1431306493t_bool] :
      ( hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_2)),hAPP_b128655177t_bool(B_1,X_2))) ) ) ).

tff(fact_164_Pi__mem,axiom,
    ! [X_2: nat,F: fun_na296811289t_bool,A_1: fun_nat_bool,B_1: fun_na6909291l_bool] :
      ( hBOOL(hAPP_f1910182691l_bool(hAPP_f1251101421l_bool(member1931034374t_bool,F),pi_nat1489913205t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_n2138229611t_bool(F,X_2)),hAPP_n2125602947l_bool(B_1,X_2))) ) ) ).

tff(fact_165_Pi__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr908190898t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_Pr1204542610l_bool] :
      ( hBOOL(hAPP_f715770888l_bool(hAPP_f1658660365l_bool(member234726149t_bool,F),pi_Pro606697670t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P94229072t_bool(F,X_2)),hAPP_P878768990l_bool(B_1,X_2))) ) ) ).

tff(fact_166_Pi__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar1623257374t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_Ar59992358l_bool] :
      ( hBOOL(hAPP_f1709974824l_bool(hAPP_f2017976695l_bool(member870521227t_bool,F),pi_Arr220620154t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(F,X_2)),hAPP_A850178878l_bool(B_1,X_2))) ) ) ).

tff(fact_167_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar624010239t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1998664965l_bool] :
      ( hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_2)),hAPP_A1411662545l_bool(B_1,X_2))) ) ) ).

tff(fact_168_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo1476023096t_bool,A_1: fun_bool_bool,B_1: fun_bo2107365004l_bool] :
      ( hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_2)),hAPP_b1078573912l_bool(B_1,X_2))) ) ) ).

tff(fact_169_Pi__mem,axiom,
    ! [X_2: nat,F: fun_na998785244t_bool,A_1: fun_nat_bool,B_1: fun_na144630978l_bool] :
      ( hBOOL(hAPP_f2035897138l_bool(hAPP_f826277901l_bool(member883057071t_bool,F),pi_nat1942897898t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_n1161265524t_bool(F,X_2)),hAPP_n1134275860l_bool(B_1,X_2))) ) ) ).

tff(fact_170_Pi__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr324456707t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_Pr80661467l_bool] :
      ( hBOOL(hAPP_f573096205l_bool(hAPP_f2100194497l_bool(member1190141424t_bool,F),pi_Pro469835097t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1708597583t_bool(F,X_2)),hAPP_P171164537l_bool(B_1,X_2))) ) ) ).

tff(fact_171_Pi__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar1573071255t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_Ar339057223l_bool] :
      ( hBOOL(hAPP_f1590435821l_bool(hAPP_f467104333l_bool(member144328170t_bool,F),pi_Arr192316325t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(F,X_2)),hAPP_A442239897l_bool(B_1,X_2))) ) ) ).

tff(fact_172_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo1431306493t_bool,A_1: fun_bool_bool,B_1: fun_bo377688929l_bool] :
      ( hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_2)),hAPP_b1272691967l_bool(B_1,X_2))) ) ) ).

tff(fact_173_Pi__mem,axiom,
    ! [X_2: nat,F: fun_na2092219207t_bool,A_1: fun_nat_bool,B_1: fun_na138495129l_bool] :
      ( hBOOL(hAPP_f562872145l_bool(hAPP_f517158217l_bool(member1683162164t_bool,F),pi_nat608045987t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_n2091767705t_bool(F,X_2)),hAPP_n1555388849l_bool(B_1,X_2))) ) ) ).

tff(fact_174_Pi__mem,axiom,
    ! [X_2: produc587761367le_alt,F: fun_Pr1188951520t_bool,A_1: fun_Pr486337689t_bool,B_1: fun_Pr1411261120l_bool] :
      ( hBOOL(hAPP_f1470281014l_bool(hAPP_f666236045l_bool(member1431564083t_bool,F),pi_Pro87132148t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P50207614t_bool(F,X_2)),hAPP_P1986703244l_bool(B_1,X_2))) ) ) ).

tff(fact_175_Pi__mem,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar248516172t_bool,A_1: fun_Ar17477381t_bool,B_1: fun_Ar1071883092l_bool] :
      ( hBOOL(hAPP_f585444950l_bool(hAPP_f868830675l_bool(member346602425t_bool,F),pi_Arr494635176t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1610503070t_bool(F,X_2)),hAPP_A1569148780l_bool(B_1,X_2))) ) ) ).

tff(fact_176_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar286530093t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1321653811l_bool] :
      ( hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_2)),hAPP_A2084592127l_bool(B_1,X_2))) ) ) ).

tff(fact_177_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo559790694t_bool,A_1: fun_bool_bool,B_1: fun_bo1445676730l_bool] :
      ( hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_2)),hAPP_b1777246598l_bool(B_1,X_2))) ) ) ).

tff(fact_178_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu2114379172t_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu1863781882l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_2)),hAPP_f1915815064l_bool(B_1,X_2))) ) ) ).

tff(fact_179_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar274636406t_bool,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1474557608l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_2)),hAPP_A897398598l_bool(B_1,X_2))) ) ) ).

tff(fact_180_Pi__I,axiom,
    ! [F: fun_Pr392309332lt_nat,B_1: fun_Pr428964044t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P923196832lt_nat(F,X_1)),hAPP_P1123315306t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f69887326l_bool(hAPP_f1736181859l_bool(member1130928449lt_nat,F),pi_Pro847445418lt_nat(A_1,B_1))) ) ).

tff(fact_181_Pi__I,axiom,
    ! [F: fun_Pr139923747le_alt,B_1: fun_Pr1701595235t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_P2117677505le_alt(F,X_1)),hAPP_P588680495t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f963889529l_bool(hAPP_f1110468429l_bool(member1449157750le_alt,F),pi_Pro910144055le_alt(A_1,B_1))) ) ).

tff(fact_182_Pi__I,axiom,
    ! [F: fun_Pr1196455769le_alt,B_1: fun_Pr1407669585t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_P909886117le_alt(F,X_1)),hAPP_P1328248815t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f125423203l_bool(hAPP_f434978669l_bool(member902318790le_alt,F),pi_Pro262333359le_alt(A_1,B_1))) ) ).

tff(fact_183_Pi__I,axiom,
    ! [F: fun_Pr1509342064e_indi,B_1: fun_Pr895221296i_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_1)),hAPP_P1859429372i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A_1,B_1))) ) ).

tff(fact_184_Pi__I,axiom,
    ! [F: fun_fu1616460421ol_nat,B_1: fun_fu1077134171t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1262704593ol_nat(F,X_1)),hAPP_f595382009t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f462751375l_bool(hAPP_f1774924229l_bool(member1103199858ol_nat,F),pi_fun614388187ol_nat(A_1,B_1))) ) ).

tff(fact_185_Pi__I,axiom,
    ! [F: fun_fu1228726322le_alt,B_1: fun_fu1258557076t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f133306064le_alt(F,X_1)),hAPP_f1745861984t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1673349000l_bool(hAPP_f1710130701l_bool(member555261573le_alt,F),pi_fun645774662le_alt(A_1,B_1))) ) ).

tff(fact_186_Pi__I,axiom,
    ! [F: fun_fu1224779274le_alt,B_1: fun_fu2143707488t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f1965185878le_alt(F,X_1)),hAPP_f1841273342t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1789660692l_bool(hAPP_f650195279l_bool(member472043127le_alt,F),pi_fun1760679520le_alt(A_1,B_1))) ) ).

tff(fact_187_Pi__I,axiom,
    ! [F: fun_fu1929591039e_indi,B_1: fun_fu223278561i_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_1)),hAPP_f391644589i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A_1,B_1))) ) ).

tff(fact_188_Pi__I,axiom,
    ! [F: fun_fu3835832l_bool,B_1: fun_fu916327706l_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_1)),hAPP_f1676084198l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A_1,B_1))) ) ).

tff(fact_189_Pi__I,axiom,
    ! [F: fun_fu841105374ol_nat,B_1: fun_fu477456066t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1842225014ol_nat(F,X_1)),hAPP_f703394068t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f461570100l_bool(hAPP_f1175388045l_bool(member725377201ol_nat,F),pi_fun476373740ol_nat(A_1,B_1))) ) ).

tff(fact_190_Pi__I,axiom,
    ! [F: fun_fu1431796761le_alt,B_1: fun_fu1924348397t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f1273325419le_alt(F,X_1)),hAPP_f369701637t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f288351779l_bool(hAPP_f1909282029l_bool(member149997830le_alt,F),pi_fun34562933le_alt(A_1,B_1))) ) ).

tff(fact_191_Pi__I,axiom,
    ! [F: fun_fu67587555le_alt,B_1: fun_fu1534804551t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f773337979le_alt(F,X_1)),hAPP_f234621849t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f730470457l_bool(hAPP_f1494675789l_bool(member786328118le_alt,F),pi_fun1511699953le_alt(A_1,B_1))) ) ).

tff(fact_192_Pi__I,axiom,
    ! [F: fun_fu562005862e_indi,B_1: fun_fu2142850746i_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_1)),hAPP_f2010315474i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A_1,B_1))) ) ).

tff(fact_193_Pi__I,axiom,
    ! [F: fun_fu638310559l_bool,B_1: fun_fu237781875l_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_1)),hAPP_f463104139l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A_1,B_1))) ) ).

tff(fact_194_Pi__I,axiom,
    ! [F: fun_fu60852439ol_nat,B_1: fun_fu1667513993t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1333555235ol_nat(F,X_1)),hAPP_f1550778407t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1661238497l_bool(hAPP_f996655209l_bool(member1799279044ol_nat,F),pi_fun1997317165ol_nat(A_1,B_1))) ) ).

tff(fact_195_Pi__I,axiom,
    ! [F: fun_fu356555872le_alt,B_1: fun_fu2050451686t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f257198334le_alt(F,X_1)),hAPP_f210821554t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2015026102l_bool(hAPP_f1071682701l_bool(member599168435le_alt,F),pi_fun294122868le_alt(A_1,B_1))) ) ).

tff(fact_196_Pi__I,axiom,
    ! [F: fun_fu71747932le_alt,B_1: fun_fu1566951310t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f398149800le_alt(F,X_1)),hAPP_f2038412844t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f975067494l_bool(hAPP_f1946164211l_bool(member169834185le_alt,F),pi_fun1429765554le_alt(A_1,B_1))) ) ).

tff(fact_197_Pi__I,axiom,
    ! [F: fun_fu748153389e_indi,B_1: fun_fu2109152051i_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_1)),hAPP_f399308031i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A_1,B_1))) ) ).

tff(fact_198_Pi__I,axiom,
    ! [F: fun_fu2098777574l_bool,B_1: fun_fu1522163052l_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_1)),hAPP_f414129720l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A_1,B_1))) ) ).

tff(fact_199_Pi__I,axiom,
    ! [F: fun_na654729482le_alt,B_1: fun_na998785244t_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_n216724700le_alt(F,X_1)),hAPP_n1161265524t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f237532692l_bool(hAPP_f1907966927l_bool(member1393348599le_alt,F),pi_nat140973286le_alt(A_1,B_1))) ) ).

tff(fact_200_Pi__I,axiom,
    ! [F: fun_Pr1116498339le_alt,B_1: fun_Pr324456707t_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P211644097le_alt(F,X_1)),hAPP_P1708597583t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1446814201l_bool(hAPP_f141330253l_bool(member278248694le_alt,F),pi_Pro1151594295le_alt(A_1,B_1))) ) ).

tff(fact_201_Pi__I,axiom,
    ! [F: fun_Ar245737999le_alt,B_1: fun_Ar1573071255t_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(F,X_1)),hAPP_A1601437999t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f583850777l_bool(hAPP_f109138393l_bool(member2099084668le_alt,F),pi_Arr651462635le_alt(A_1,B_1))) ) ).

tff(fact_202_Pi__I,axiom,
    ! [F: fun_Ar338949104le_alt,B_1: fun_Ar274636406t_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_1)),hAPP_A1646126530t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A_1,B_1))) ) ).

tff(fact_203_Pi__I,axiom,
    ! [F: fun_bo1682907689le_alt,B_1: fun_bo1431306493t_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_1)),hAPP_b128655177t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A_1,B_1))) ) ).

tff(fact_204_Pi__I,axiom,
    ! [F: fun_na296811289t_bool,B_1: fun_na6909291l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_n2138229611t_bool(F,X_1)),hAPP_n2125602947l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1910182691l_bool(hAPP_f1251101421l_bool(member1931034374t_bool,F),pi_nat1489913205t_bool(A_1,B_1))) ) ).

tff(fact_205_Pi__I,axiom,
    ! [F: fun_Pr908190898t_bool,B_1: fun_Pr1204542610l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P94229072t_bool(F,X_1)),hAPP_P878768990l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f715770888l_bool(hAPP_f1658660365l_bool(member234726149t_bool,F),pi_Pro606697670t_bool(A_1,B_1))) ) ).

tff(fact_206_Pi__I,axiom,
    ! [F: fun_Ar1623257374t_bool,B_1: fun_Ar59992358l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(F,X_1)),hAPP_A850178878l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1709974824l_bool(hAPP_f2017976695l_bool(member870521227t_bool,F),pi_Arr220620154t_bool(A_1,B_1))) ) ).

tff(fact_207_Pi__I,axiom,
    ! [F: fun_Ar624010239t_bool,B_1: fun_Ar1998664965l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_1)),hAPP_A1411662545l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A_1,B_1))) ) ).

tff(fact_208_Pi__I,axiom,
    ! [F: fun_bo1476023096t_bool,B_1: fun_bo2107365004l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_1)),hAPP_b1078573912l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A_1,B_1))) ) ).

tff(fact_209_Pi__I,axiom,
    ! [F: fun_na998785244t_bool,B_1: fun_na144630978l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_n1161265524t_bool(F,X_1)),hAPP_n1134275860l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2035897138l_bool(hAPP_f826277901l_bool(member883057071t_bool,F),pi_nat1942897898t_bool(A_1,B_1))) ) ).

tff(fact_210_Pi__I,axiom,
    ! [F: fun_Pr324456707t_bool,B_1: fun_Pr80661467l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1708597583t_bool(F,X_1)),hAPP_P171164537l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f573096205l_bool(hAPP_f2100194497l_bool(member1190141424t_bool,F),pi_Pro469835097t_bool(A_1,B_1))) ) ).

tff(fact_211_Pi__I,axiom,
    ! [F: fun_Ar1573071255t_bool,B_1: fun_Ar339057223l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(F,X_1)),hAPP_A442239897l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1590435821l_bool(hAPP_f467104333l_bool(member144328170t_bool,F),pi_Arr192316325t_bool(A_1,B_1))) ) ).

tff(fact_212_Pi__I,axiom,
    ! [F: fun_bo1431306493t_bool,B_1: fun_bo377688929l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_1)),hAPP_b1272691967l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A_1,B_1))) ) ).

tff(fact_213_Pi__I,axiom,
    ! [F: fun_na2092219207t_bool,B_1: fun_na138495129l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_n2091767705t_bool(F,X_1)),hAPP_n1555388849l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f562872145l_bool(hAPP_f517158217l_bool(member1683162164t_bool,F),pi_nat608045987t_bool(A_1,B_1))) ) ).

tff(fact_214_Pi__I,axiom,
    ! [F: fun_Pr1188951520t_bool,B_1: fun_Pr1411261120l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P50207614t_bool(F,X_1)),hAPP_P1986703244l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1470281014l_bool(hAPP_f666236045l_bool(member1431564083t_bool,F),pi_Pro87132148t_bool(A_1,B_1))) ) ).

tff(fact_215_Pi__I,axiom,
    ! [F: fun_Ar248516172t_bool,B_1: fun_Ar1071883092l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1610503070t_bool(F,X_1)),hAPP_A1569148780l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f585444950l_bool(hAPP_f868830675l_bool(member346602425t_bool,F),pi_Arr494635176t_bool(A_1,B_1))) ) ).

tff(fact_216_Pi__I,axiom,
    ! [F: fun_Ar286530093t_bool,B_1: fun_Ar1321653811l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_1)),hAPP_A2084592127l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A_1,B_1))) ) ).

tff(fact_217_Pi__I,axiom,
    ! [F: fun_bo559790694t_bool,B_1: fun_bo1445676730l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_1)),hAPP_b1777246598l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A_1,B_1))) ) ).

tff(fact_218_Pi__I,axiom,
    ! [F: fun_Pr2067565481t_bool,B_1: fun_Pr1780397033l_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_1)),hAPP_P1103642805l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,B_1))) ) ).

tff(fact_219_Pi__I,axiom,
    ! [F: fun_fu2114379172t_bool,B_1: fun_fu1863781882l_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_1)),hAPP_f1915815064l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,B_1))) ) ).

tff(fact_220_Pi__I,axiom,
    ! [F: fun_Ar274636406t_bool,B_1: fun_Ar1474557608l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_1)),hAPP_A897398598l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,B_1))) ) ).

tff(fact_221_funcsetI,axiom,
    ! [F: fun_Pr392309332lt_nat,B_1: fun_nat_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P923196832lt_nat(F,X_1)),B_1)) )
     => hBOOL(hAPP_f69887326l_bool(hAPP_f1736181859l_bool(member1130928449lt_nat,F),pi_Pro847445418lt_nat(A_1,hAPP_f795770633t_bool(cOMBK_1524165667le_alt,B_1)))) ) ).

tff(fact_222_funcsetI,axiom,
    ! [F: fun_Pr139923747le_alt,B_1: fun_Pr486337689t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_P2117677505le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f963889529l_bool(hAPP_f1110468429l_bool(member1449157750le_alt,F),pi_Pro910144055le_alt(A_1,hAPP_f480827367t_bool(cOMBK_605104626le_alt,B_1)))) ) ).

tff(fact_223_funcsetI,axiom,
    ! [F: fun_Pr1196455769le_alt,B_1: fun_Ar17477381t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_P909886117le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f125423203l_bool(hAPP_f434978669l_bool(member902318790le_alt,F),pi_Pro262333359le_alt(A_1,hAPP_f1074682185t_bool(cOMBK_385683240le_alt,B_1)))) ) ).

tff(fact_224_funcsetI,axiom,
    ! [F: fun_Pr1509342064e_indi,B_1: fun_Ar1809396326i_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_1)),B_1)) )
     => hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A_1,hAPP_f359069313i_bool(cOMBK_1987648063le_alt,B_1)))) ) ).

tff(fact_225_funcsetI,axiom,
    ! [F: fun_fu1616460421ol_nat,B_1: fun_nat_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1262704593ol_nat(F,X_1)),B_1)) )
     => hBOOL(hAPP_f462751375l_bool(hAPP_f1774924229l_bool(member1103199858ol_nat,F),pi_fun614388187ol_nat(A_1,hAPP_f1195142808t_bool(cOMBK_155500978t_bool,B_1)))) ) ).

tff(fact_226_funcsetI,axiom,
    ! [F: fun_fu1228726322le_alt,B_1: fun_Pr486337689t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f133306064le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1673349000l_bool(hAPP_f1710130701l_bool(member555261573le_alt,F),pi_fun645774662le_alt(A_1,hAPP_f2020753944t_bool(cOMBK_342345345t_bool,B_1)))) ) ).

tff(fact_227_funcsetI,axiom,
    ! [F: fun_fu1224779274le_alt,B_1: fun_Ar17477381t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f1965185878le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1789660692l_bool(hAPP_f650195279l_bool(member472043127le_alt,F),pi_fun1760679520le_alt(A_1,hAPP_f1027939672t_bool(cOMBK_1334022583t_bool,B_1)))) ) ).

tff(fact_228_funcsetI,axiom,
    ! [F: fun_fu1929591039e_indi,B_1: fun_Ar1809396326i_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_1)),B_1)) )
     => hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A_1,hAPP_f2022065970i_bool(cOMBK_818801614t_bool,B_1)))) ) ).

tff(fact_229_funcsetI,axiom,
    ! [F: fun_fu3835832l_bool,B_1: fun_bool_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A_1,hAPP_f1582869284l_bool(cOMBK_542452487t_bool,B_1)))) ) ).

tff(fact_230_funcsetI,axiom,
    ! [F: fun_fu841105374ol_nat,B_1: fun_nat_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1842225014ol_nat(F,X_1)),B_1)) )
     => hBOOL(hAPP_f461570100l_bool(hAPP_f1175388045l_bool(member725377201ol_nat,F),pi_fun476373740ol_nat(A_1,hAPP_f779832389t_bool(cOMBK_198318445t_bool,B_1)))) ) ).

tff(fact_231_funcsetI,axiom,
    ! [F: fun_fu1431796761le_alt,B_1: fun_Pr486337689t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f1273325419le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f288351779l_bool(hAPP_f1909282029l_bool(member149997830le_alt,F),pi_fun34562933le_alt(A_1,hAPP_f1369154921t_bool(cOMBK_1697579230t_bool,B_1)))) ) ).

tff(fact_232_funcsetI,axiom,
    ! [F: fun_fu67587555le_alt,B_1: fun_Ar17477381t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f773337979le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f730470457l_bool(hAPP_f1494675789l_bool(member786328118le_alt,F),pi_fun1511699953le_alt(A_1,hAPP_f1227262031t_bool(cOMBK_837265448t_bool,B_1)))) ) ).

tff(fact_233_funcsetI,axiom,
    ! [F: fun_fu562005862e_indi,B_1: fun_Ar1809396326i_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_1)),B_1)) )
     => hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A_1,hAPP_f1128827177i_bool(cOMBK_814147665t_bool,B_1)))) ) ).

tff(fact_234_funcsetI,axiom,
    ! [F: fun_fu638310559l_bool,B_1: fun_bool_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A_1,hAPP_f1713038057l_bool(cOMBK_118864600t_bool,B_1)))) ) ).

tff(fact_235_funcsetI,axiom,
    ! [F: fun_fu60852439ol_nat,B_1: fun_nat_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1333555235ol_nat(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1661238497l_bool(hAPP_f996655209l_bool(member1799279044ol_nat,F),pi_fun1997317165ol_nat(A_1,hAPP_f1319616198t_bool(cOMBK_2008571104t_bool,B_1)))) ) ).

tff(fact_236_funcsetI,axiom,
    ! [F: fun_fu356555872le_alt,B_1: fun_Pr486337689t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f257198334le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f2015026102l_bool(hAPP_f1071682701l_bool(member599168435le_alt,F),pi_fun294122868le_alt(A_1,hAPP_f2065367146t_bool(cOMBK_1118451887t_bool,B_1)))) ) ).

tff(fact_237_funcsetI,axiom,
    ! [F: fun_fu71747932le_alt,B_1: fun_Ar17477381t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f398149800le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f975067494l_bool(hAPP_f1946164211l_bool(member169834185le_alt,F),pi_fun1429765554le_alt(A_1,hAPP_f1552202630t_bool(cOMBK_1544325605t_bool,B_1)))) ) ).

tff(fact_238_funcsetI,axiom,
    ! [F: fun_fu748153389e_indi,B_1: fun_Ar1809396326i_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_1)),B_1)) )
     => hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A_1,hAPP_f448050564i_bool(cOMBK_443335420t_bool,B_1)))) ) ).

tff(fact_239_funcsetI,axiom,
    ! [F: fun_fu2098777574l_bool,B_1: fun_bool_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A_1,hAPP_f1152234870l_bool(cOMBK_1770320693t_bool,B_1)))) ) ).

tff(fact_240_funcsetI,axiom,
    ! [F: fun_na654729482le_alt,B_1: fun_Pr2067565481t_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_n216724700le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f237532692l_bool(hAPP_f1907966927l_bool(member1393348599le_alt,F),pi_nat140973286le_alt(A_1,hAPP_f1409698632t_bool(cOMBK_1882555695ol_nat,B_1)))) ) ).

tff(fact_241_funcsetI,axiom,
    ! [F: fun_Pr1116498339le_alt,B_1: fun_Pr2067565481t_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P211644097le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1446814201l_bool(hAPP_f141330253l_bool(member278248694le_alt,F),pi_Pro1151594295le_alt(A_1,hAPP_f1290118551t_bool(cOMBK_1555225330le_alt,B_1)))) ) ).

tff(fact_242_funcsetI,axiom,
    ! [F: fun_Ar245737999le_alt,B_1: fun_Pr2067565481t_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f583850777l_bool(hAPP_f109138393l_bool(member2099084668le_alt,F),pi_Arr651462635le_alt(A_1,hAPP_f1761571331t_bool(cOMBK_392407988le_alt,B_1)))) ) ).

tff(fact_243_funcsetI,axiom,
    ! [F: fun_Ar338949104le_alt,B_1: fun_Pr2067565481t_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A_1,hAPP_f480276746t_bool(cOMBK_1650320063e_indi,B_1)))) ) ).

tff(fact_244_funcsetI,axiom,
    ! [F: fun_bo1682907689le_alt,B_1: fun_Pr2067565481t_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A_1,hAPP_f1723896209t_bool(cOMBK_5056120l_bool,B_1)))) ) ).

tff(fact_245_funcsetI,axiom,
    ! [F: fun_na296811289t_bool,B_1: fun_fu3835832l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_n2138229611t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1910182691l_bool(hAPP_f1251101421l_bool(member1931034374t_bool,F),pi_nat1489913205t_bool(A_1,hAPP_f784815496l_bool(cOMBK_238368224ol_nat,B_1)))) ) ).

tff(fact_246_funcsetI,axiom,
    ! [F: fun_Pr908190898t_bool,B_1: fun_fu3835832l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P94229072t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f715770888l_bool(hAPP_f1658660365l_bool(member234726149t_bool,F),pi_Pro606697670t_bool(A_1,hAPP_f1465094837l_bool(cOMBK_448375169le_alt,B_1)))) ) ).

tff(fact_247_funcsetI,axiom,
    ! [F: fun_Ar1623257374t_bool,B_1: fun_fu3835832l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1709974824l_bool(hAPP_f2017976695l_bool(member870521227t_bool,F),pi_Arr220620154t_bool(A_1,hAPP_f1173384643l_bool(cOMBK_757054181le_alt,B_1)))) ) ).

tff(fact_248_funcsetI,axiom,
    ! [F: fun_Ar624010239t_bool,B_1: fun_fu3835832l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A_1,hAPP_f1352816552l_bool(cOMBK_1255579598e_indi,B_1)))) ) ).

tff(fact_249_funcsetI,axiom,
    ! [F: fun_bo1476023096t_bool,B_1: fun_fu3835832l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A_1,hAPP_f1322579375l_bool(cOMBK_317366791l_bool,B_1)))) ) ).

tff(fact_250_funcsetI,axiom,
    ! [F: fun_na998785244t_bool,B_1: fun_fu638310559l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_n1161265524t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f2035897138l_bool(hAPP_f826277901l_bool(member883057071t_bool,F),pi_nat1942897898t_bool(A_1,hAPP_f1191475300l_bool(cOMBK_214082799ol_nat,B_1)))) ) ).

tff(fact_251_funcsetI,axiom,
    ! [F: fun_Pr324456707t_bool,B_1: fun_fu638310559l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1708597583t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f573096205l_bool(hAPP_f2100194497l_bool(member1190141424t_bool,F),pi_Pro469835097t_bool(A_1,hAPP_f908691129l_bool(cOMBK_1807543090le_alt,B_1)))) ) ).

tff(fact_252_funcsetI,axiom,
    ! [F: fun_Ar1573071255t_bool,B_1: fun_fu638310559l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1590435821l_bool(hAPP_f467104333l_bool(member144328170t_bool,F),pi_Arr192316325t_bool(A_1,hAPP_f1301449449l_bool(cOMBK_935799668le_alt,B_1)))) ) ).

tff(fact_253_funcsetI,axiom,
    ! [F: fun_bo1431306493t_bool,B_1: fun_fu638310559l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A_1,hAPP_f86272063l_bool(cOMBK_650639032l_bool,B_1)))) ) ).

tff(fact_254_funcsetI,axiom,
    ! [F: fun_na2092219207t_bool,B_1: fun_fu2098777574l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_n2091767705t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f562872145l_bool(hAPP_f517158217l_bool(member1683162164t_bool,F),pi_nat608045987t_bool(A_1,hAPP_f1268543752l_bool(cOMBK_1485688882ol_nat,B_1)))) ) ).

tff(fact_255_funcsetI,axiom,
    ! [F: fun_Pr1188951520t_bool,B_1: fun_fu2098777574l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P50207614t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1470281014l_bool(hAPP_f666236045l_bool(member1431564083t_bool,F),pi_Pro87132148t_bool(A_1,hAPP_f852696849l_bool(cOMBK_1524832687le_alt,B_1)))) ) ).

tff(fact_256_funcsetI,axiom,
    ! [F: fun_Ar248516172t_bool,B_1: fun_fu2098777574l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1610503070t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f585444950l_bool(hAPP_f868830675l_bool(member346602425t_bool,F),pi_Arr494635176t_bool(A_1,hAPP_f1933295939l_bool(cOMBK_1583688247le_alt,B_1)))) ) ).

tff(fact_257_funcsetI,axiom,
    ! [F: fun_Ar286530093t_bool,B_1: fun_fu2098777574l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A_1,hAPP_f258290692l_bool(cOMBK_1514079484e_indi,B_1)))) ) ).

tff(fact_258_funcsetI,axiom,
    ! [F: fun_bo559790694t_bool,B_1: fun_fu2098777574l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A_1,hAPP_f369767947l_bool(cOMBK_2030738485l_bool,B_1)))) ) ).

tff(fact_259_funcsetI,axiom,
    ! [F: fun_Pr2067565481t_bool,B_1: fun_bool_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,hAPP_f699791347l_bool(cOMBK_138598520le_alt,B_1)))) ) ).

tff(fact_260_funcsetI,axiom,
    ! [F: fun_fu2114379172t_bool,B_1: fun_fu638310559l_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,B_1)))) ) ).

tff(fact_261_funcsetI,axiom,
    ! [F: fun_Ar274636406t_bool,B_1: fun_fu638310559l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_1)),B_1)) )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,B_1)))) ) ).

tff(fact_262_Pi__I_H,axiom,
    ! [F: fun_Pr392309332lt_nat,B_1: fun_Pr428964044t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P923196832lt_nat(F,X_1)),hAPP_P1123315306t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f69887326l_bool(hAPP_f1736181859l_bool(member1130928449lt_nat,F),pi_Pro847445418lt_nat(A_1,B_1))) ) ).

tff(fact_263_Pi__I_H,axiom,
    ! [F: fun_Pr139923747le_alt,B_1: fun_Pr1701595235t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_P2117677505le_alt(F,X_1)),hAPP_P588680495t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f963889529l_bool(hAPP_f1110468429l_bool(member1449157750le_alt,F),pi_Pro910144055le_alt(A_1,B_1))) ) ).

tff(fact_264_Pi__I_H,axiom,
    ! [F: fun_Pr1196455769le_alt,B_1: fun_Pr1407669585t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_P909886117le_alt(F,X_1)),hAPP_P1328248815t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f125423203l_bool(hAPP_f434978669l_bool(member902318790le_alt,F),pi_Pro262333359le_alt(A_1,B_1))) ) ).

tff(fact_265_Pi__I_H,axiom,
    ! [F: fun_Pr1509342064e_indi,B_1: fun_Pr895221296i_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_1)),hAPP_P1859429372i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A_1,B_1))) ) ).

tff(fact_266_Pi__I_H,axiom,
    ! [F: fun_fu1616460421ol_nat,B_1: fun_fu1077134171t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1262704593ol_nat(F,X_1)),hAPP_f595382009t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f462751375l_bool(hAPP_f1774924229l_bool(member1103199858ol_nat,F),pi_fun614388187ol_nat(A_1,B_1))) ) ).

tff(fact_267_Pi__I_H,axiom,
    ! [F: fun_fu1228726322le_alt,B_1: fun_fu1258557076t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f133306064le_alt(F,X_1)),hAPP_f1745861984t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1673349000l_bool(hAPP_f1710130701l_bool(member555261573le_alt,F),pi_fun645774662le_alt(A_1,B_1))) ) ).

tff(fact_268_Pi__I_H,axiom,
    ! [F: fun_fu1224779274le_alt,B_1: fun_fu2143707488t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f1965185878le_alt(F,X_1)),hAPP_f1841273342t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1789660692l_bool(hAPP_f650195279l_bool(member472043127le_alt,F),pi_fun1760679520le_alt(A_1,B_1))) ) ).

tff(fact_269_Pi__I_H,axiom,
    ! [F: fun_fu1929591039e_indi,B_1: fun_fu223278561i_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_1)),hAPP_f391644589i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A_1,B_1))) ) ).

tff(fact_270_Pi__I_H,axiom,
    ! [F: fun_fu3835832l_bool,B_1: fun_fu916327706l_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_1)),hAPP_f1676084198l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A_1,B_1))) ) ).

tff(fact_271_Pi__I_H,axiom,
    ! [F: fun_fu841105374ol_nat,B_1: fun_fu477456066t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1842225014ol_nat(F,X_1)),hAPP_f703394068t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f461570100l_bool(hAPP_f1175388045l_bool(member725377201ol_nat,F),pi_fun476373740ol_nat(A_1,B_1))) ) ).

tff(fact_272_Pi__I_H,axiom,
    ! [F: fun_fu1431796761le_alt,B_1: fun_fu1924348397t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f1273325419le_alt(F,X_1)),hAPP_f369701637t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f288351779l_bool(hAPP_f1909282029l_bool(member149997830le_alt,F),pi_fun34562933le_alt(A_1,B_1))) ) ).

tff(fact_273_Pi__I_H,axiom,
    ! [F: fun_fu67587555le_alt,B_1: fun_fu1534804551t_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f773337979le_alt(F,X_1)),hAPP_f234621849t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f730470457l_bool(hAPP_f1494675789l_bool(member786328118le_alt,F),pi_fun1511699953le_alt(A_1,B_1))) ) ).

tff(fact_274_Pi__I_H,axiom,
    ! [F: fun_fu562005862e_indi,B_1: fun_fu2142850746i_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_1)),hAPP_f2010315474i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A_1,B_1))) ) ).

tff(fact_275_Pi__I_H,axiom,
    ! [F: fun_fu638310559l_bool,B_1: fun_fu237781875l_bool,A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_1)),hAPP_f463104139l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A_1,B_1))) ) ).

tff(fact_276_Pi__I_H,axiom,
    ! [F: fun_fu60852439ol_nat,B_1: fun_fu1667513993t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1333555235ol_nat(F,X_1)),hAPP_f1550778407t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1661238497l_bool(hAPP_f996655209l_bool(member1799279044ol_nat,F),pi_fun1997317165ol_nat(A_1,B_1))) ) ).

tff(fact_277_Pi__I_H,axiom,
    ! [F: fun_fu356555872le_alt,B_1: fun_fu2050451686t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_f257198334le_alt(F,X_1)),hAPP_f210821554t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2015026102l_bool(hAPP_f1071682701l_bool(member599168435le_alt,F),pi_fun294122868le_alt(A_1,B_1))) ) ).

tff(fact_278_Pi__I_H,axiom,
    ! [F: fun_fu71747932le_alt,B_1: fun_fu1566951310t_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hAPP_f398149800le_alt(F,X_1)),hAPP_f2038412844t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f975067494l_bool(hAPP_f1946164211l_bool(member169834185le_alt,F),pi_fun1429765554le_alt(A_1,B_1))) ) ).

tff(fact_279_Pi__I_H,axiom,
    ! [F: fun_fu748153389e_indi,B_1: fun_fu2109152051i_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_1)),hAPP_f399308031i_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A_1,B_1))) ) ).

tff(fact_280_Pi__I_H,axiom,
    ! [F: fun_fu2098777574l_bool,B_1: fun_fu1522163052l_bool,A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_1)),hAPP_f414129720l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A_1,B_1))) ) ).

tff(fact_281_Pi__I_H,axiom,
    ! [F: fun_na654729482le_alt,B_1: fun_na998785244t_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_n216724700le_alt(F,X_1)),hAPP_n1161265524t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f237532692l_bool(hAPP_f1907966927l_bool(member1393348599le_alt,F),pi_nat140973286le_alt(A_1,B_1))) ) ).

tff(fact_282_Pi__I_H,axiom,
    ! [F: fun_Pr1116498339le_alt,B_1: fun_Pr324456707t_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P211644097le_alt(F,X_1)),hAPP_P1708597583t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1446814201l_bool(hAPP_f141330253l_bool(member278248694le_alt,F),pi_Pro1151594295le_alt(A_1,B_1))) ) ).

tff(fact_283_Pi__I_H,axiom,
    ! [F: fun_Ar245737999le_alt,B_1: fun_Ar1573071255t_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(F,X_1)),hAPP_A1601437999t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f583850777l_bool(hAPP_f109138393l_bool(member2099084668le_alt,F),pi_Arr651462635le_alt(A_1,B_1))) ) ).

tff(fact_284_Pi__I_H,axiom,
    ! [F: fun_Ar338949104le_alt,B_1: fun_Ar274636406t_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_1)),hAPP_A1646126530t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A_1,B_1))) ) ).

tff(fact_285_Pi__I_H,axiom,
    ! [F: fun_bo1682907689le_alt,B_1: fun_bo1431306493t_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_1)),hAPP_b128655177t_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A_1,B_1))) ) ).

tff(fact_286_Pi__I_H,axiom,
    ! [F: fun_na296811289t_bool,B_1: fun_na6909291l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_n2138229611t_bool(F,X_1)),hAPP_n2125602947l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1910182691l_bool(hAPP_f1251101421l_bool(member1931034374t_bool,F),pi_nat1489913205t_bool(A_1,B_1))) ) ).

tff(fact_287_Pi__I_H,axiom,
    ! [F: fun_Pr908190898t_bool,B_1: fun_Pr1204542610l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P94229072t_bool(F,X_1)),hAPP_P878768990l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f715770888l_bool(hAPP_f1658660365l_bool(member234726149t_bool,F),pi_Pro606697670t_bool(A_1,B_1))) ) ).

tff(fact_288_Pi__I_H,axiom,
    ! [F: fun_Ar1623257374t_bool,B_1: fun_Ar59992358l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A425126512t_bool(F,X_1)),hAPP_A850178878l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1709974824l_bool(hAPP_f2017976695l_bool(member870521227t_bool,F),pi_Arr220620154t_bool(A_1,B_1))) ) ).

tff(fact_289_Pi__I_H,axiom,
    ! [F: fun_Ar624010239t_bool,B_1: fun_Ar1998664965l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_1)),hAPP_A1411662545l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A_1,B_1))) ) ).

tff(fact_290_Pi__I_H,axiom,
    ! [F: fun_bo1476023096t_bool,B_1: fun_bo2107365004l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_1)),hAPP_b1078573912l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A_1,B_1))) ) ).

tff(fact_291_Pi__I_H,axiom,
    ! [F: fun_na998785244t_bool,B_1: fun_na144630978l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_n1161265524t_bool(F,X_1)),hAPP_n1134275860l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f2035897138l_bool(hAPP_f826277901l_bool(member883057071t_bool,F),pi_nat1942897898t_bool(A_1,B_1))) ) ).

tff(fact_292_Pi__I_H,axiom,
    ! [F: fun_Pr324456707t_bool,B_1: fun_Pr80661467l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1708597583t_bool(F,X_1)),hAPP_P171164537l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f573096205l_bool(hAPP_f2100194497l_bool(member1190141424t_bool,F),pi_Pro469835097t_bool(A_1,B_1))) ) ).

tff(fact_293_Pi__I_H,axiom,
    ! [F: fun_Ar1573071255t_bool,B_1: fun_Ar339057223l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(F,X_1)),hAPP_A442239897l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1590435821l_bool(hAPP_f467104333l_bool(member144328170t_bool,F),pi_Arr192316325t_bool(A_1,B_1))) ) ).

tff(fact_294_Pi__I_H,axiom,
    ! [F: fun_bo1431306493t_bool,B_1: fun_bo377688929l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_1)),hAPP_b1272691967l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A_1,B_1))) ) ).

tff(fact_295_Pi__I_H,axiom,
    ! [F: fun_na2092219207t_bool,B_1: fun_na138495129l_bool,A_1: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_n2091767705t_bool(F,X_1)),hAPP_n1555388849l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f562872145l_bool(hAPP_f517158217l_bool(member1683162164t_bool,F),pi_nat608045987t_bool(A_1,B_1))) ) ).

tff(fact_296_Pi__I_H,axiom,
    ! [F: fun_Pr1188951520t_bool,B_1: fun_Pr1411261120l_bool,A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P50207614t_bool(F,X_1)),hAPP_P1986703244l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1470281014l_bool(hAPP_f666236045l_bool(member1431564083t_bool,F),pi_Pro87132148t_bool(A_1,B_1))) ) ).

tff(fact_297_Pi__I_H,axiom,
    ! [F: fun_Ar248516172t_bool,B_1: fun_Ar1071883092l_bool,A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1610503070t_bool(F,X_1)),hAPP_A1569148780l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f585444950l_bool(hAPP_f868830675l_bool(member346602425t_bool,F),pi_Arr494635176t_bool(A_1,B_1))) ) ).

tff(fact_298_Pi__I_H,axiom,
    ! [F: fun_Ar286530093t_bool,B_1: fun_Ar1321653811l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_1)),hAPP_A2084592127l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A_1,B_1))) ) ).

tff(fact_299_Pi__I_H,axiom,
    ! [F: fun_bo559790694t_bool,B_1: fun_bo1445676730l_bool,A_1: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_1)),hAPP_b1777246598l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A_1,B_1))) ) ).

tff(fact_300_Pi__I_H,axiom,
    ! [F: fun_Pr2067565481t_bool,B_1: fun_Pr1780397033l_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_1)),hAPP_P1103642805l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,B_1))) ) ).

tff(fact_301_Pi__I_H,axiom,
    ! [F: fun_fu2114379172t_bool,B_1: fun_fu1863781882l_bool,A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_1)),hAPP_f1915815064l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,B_1))) ) ).

tff(fact_302_Pi__I_H,axiom,
    ! [F: fun_Ar274636406t_bool,B_1: fun_Ar1474557608l_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_1)),hAPP_A897398598l_bool(B_1,X_1))) )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,B_1))) ) ).

tff(fact_303_Pi__cong,axiom,
    ! [B_1: fun_Pr1780397033l_bool,G: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool,A_1: fun_Pr2067565481t_bool] :
      ( ! [W: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,W),A_1))
         => ( hBOOL(hAPP_P1178790471t_bool(F,W))
          <=> hBOOL(hAPP_P1178790471t_bool(G,W)) ) )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A_1,B_1)))
      <=> hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,G),pi_Pro1238944957t_bool(A_1,B_1))) ) ) ).

tff(fact_304_Pi__cong,axiom,
    ! [B_1: fun_fu1863781882l_bool,F: fun_fu2114379172t_bool,G: fun_fu2114379172t_bool,A_1: fun_fu3835832l_bool] :
      ( ! [W: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,W),A_1))
         => ( hAPP_f2008608496t_bool(F,W) = hAPP_f2008608496t_bool(G,W) ) )
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A_1,B_1)))
      <=> hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,G),pi_fun1746584570t_bool(A_1,B_1))) ) ) ).

tff(fact_305_Pi__cong,axiom,
    ! [B_1: fun_Ar1474557608l_bool,F: fun_Ar274636406t_bool,G: fun_Ar274636406t_bool,A_1: fun_Ar1809396326i_bool] :
      ( ! [W: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,W),A_1))
         => ( hAPP_A1646126530t_bool(F,W) = hAPP_A1646126530t_bool(G,W) ) )
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A_1,B_1)))
      <=> hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,G),pi_Arr959578316t_bool(A_1,B_1))) ) ) ).

tff(fact_306_PairE,axiom,
    ! [P_2: produc587761367le_alt] :
      ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] : ( P_2 != hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) ) ).

tff(fact_307_PairE,axiom,
    ! [P_2: produc472769767le_alt] :
      ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] : ( P_2 != hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) ) ).

tff(fact_308_prod_Oexhaust,axiom,
    ! [Y_13: produc587761367le_alt] :
      ~ ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] : ( Y_13 != hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6) ) ).

tff(fact_309_prod_Oexhaust,axiom,
    ! [Y_13: produc472769767le_alt] :
      ~ ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] : ( Y_13 != hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) ) ).

tff(fact_310_pred__equals__eq2,axiom,
    ! [S_1: fun_Pr486337689t_bool,R_1: fun_Pr486337689t_bool] :
      ( ! [X_1: list_A114658244le_alt,Xa: list_A114658244le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Xa)),R_1))
        <=> hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Xa)),S_1)) )
    <=> ( R_1 = S_1 ) ) ).

tff(fact_311_pred__equals__eq2,axiom,
    ! [S_1: fun_Pr2067565481t_bool,R_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: arrow_1893660431le_alt,Xa: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Xa)),R_1))
        <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Xa)),S_1)) )
    <=> ( R_1 = S_1 ) ) ).

tff(fact_312_insert__Nil,axiom,
    ! [X_36: arrow_1893660431le_alt] : ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(insert1391384533le_alt,X_36),nil_Ar557011903le_alt) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_36),nil_Ar557011903le_alt) ) ).

tff(fact_313_list__nonempty__induct,axiom,
    ! [Pa: fun_li1109619974t_bool,Xs_1: list_A114658244le_alt] :
      ( ( Xs_1 != nil_Ar557011903le_alt )
     => ( ! [X_1: arrow_1893660431le_alt] : hBOOL(hAPP_l499746980t_bool(Pa,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),nil_Ar557011903le_alt)))
       => ( ! [X_1: arrow_1893660431le_alt,Xs_17: list_A114658244le_alt] :
              ( ( Xs_17 != nil_Ar557011903le_alt )
             => ( hBOOL(hAPP_l499746980t_bool(Pa,Xs_17))
               => hBOOL(hAPP_l499746980t_bool(Pa,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Xs_17))) ) )
         => hBOOL(hAPP_l499746980t_bool(Pa,Xs_1)) ) ) ) ).

tff(fact_314_mem__def,axiom,
    ! [X_2: nat,A_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
    <=> hBOOL(hAPP_nat_bool(A_1,X_2)) ) ).

tff(fact_315_mem__def,axiom,
    ! [X_2: produc587761367le_alt,A_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
    <=> hBOOL(hAPP_P1894408759t_bool(A_1,X_2)) ) ).

tff(fact_316_mem__def,axiom,
    ! [X_2: arrow_1893660431le_alt,A_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
    <=> hBOOL(hAPP_A1748732503t_bool(A_1,X_2)) ) ).

tff(fact_317_mem__def,axiom,
    ! [X_2: arrow_856714788e_indi,A_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
    <=> hBOOL(hAPP_A997847300i_bool(A_1,X_2)) ) ).

tff(fact_318_mem__def,axiom,
    ! [X_2: bool,A_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
    <=> hBOOL(hAPP_bool_bool(A_1,X_2)) ) ).

tff(fact_319_mem__def,axiom,
    ! [X_2: produc472769767le_alt,A_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
    <=> hBOOL(hAPP_P1178790471t_bool(A_1,X_2)) ) ).

tff(fact_320_mem__def,axiom,
    ! [X_2: fun_Ar274636406t_bool,A_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
    <=> hBOOL(hAPP_f995490902l_bool(A_1,X_2)) ) ).

tff(fact_321_mem__def,axiom,
    ! [X_2: fun_Pr2067565481t_bool,A_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
    <=> hBOOL(hAPP_f52567537l_bool(A_1,X_2)) ) ).

tff(fact_322_mem__def,axiom,
    ! [X_2: fun_fu2114379172t_bool,A_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
    <=> hBOOL(hAPP_f1572141188l_bool(A_1,X_2)) ) ).

tff(fact_323_Collect__def,axiom,
    ! [Pa: fun_nat_bool] : ( collect_nat(Pa) = Pa ) ).

tff(fact_324_Collect__def,axiom,
    ! [Pa: fun_Ar17477381t_bool] : ( collec12892580le_alt(Pa) = Pa ) ).

tff(fact_325_Collect__def,axiom,
    ! [Pa: fun_Ar1809396326i_bool] : ( collec1597001935e_indi(Pa) = Pa ) ).

tff(fact_326_Collect__def,axiom,
    ! [Pa: fun_fu638310559l_bool] : ( collec2125531966t_bool(Pa) = Pa ) ).

tff(fact_327_curry__def,axiom,
    ! [X_1: fun_Pr2067565481t_bool,Xa: arrow_1893660431le_alt,Xb_1: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(produc410835390t_bool(X_1),Xa),Xb_1))
    <=> hBOOL(hAPP_P1178790471t_bool(X_1,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Xa),Xb_1))) ) ).

tff(fact_328_curryI,axiom,
    ! [F: fun_Pr486337689t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_P1894408759t_bool(F,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)))
     => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(produc1907517876t_bool(F),Aa),Ba)) ) ).

tff(fact_329_curryI,axiom,
    ! [F: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(F,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))
     => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(produc410835390t_bool(F),Aa),Ba)) ) ).

tff(fact_330_curryE,axiom,
    ! [F: fun_Pr486337689t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(produc1907517876t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P1894408759t_bool(F,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba))) ) ).

tff(fact_331_curryE,axiom,
    ! [F: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(produc410835390t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P1178790471t_bool(F,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba))) ) ).

tff(fact_332_curryD,axiom,
    ! [F: fun_Pr486337689t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(produc1907517876t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P1894408759t_bool(F,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba))) ) ).

tff(fact_333_curryD,axiom,
    ! [F: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(produc410835390t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P1178790471t_bool(F,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba))) ) ).

tff(fact_334_distinct__insert,axiom,
    ! [X_35: arrow_1893660431le_alt,Xs_49: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_49))
     => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(insert1391384533le_alt,X_35),Xs_49))) ) ).

tff(fact_335_curry__conv,axiom,
    ! [F: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(produc410835390t_bool(F),Aa),Ba))
    <=> hBOOL(hAPP_P1178790471t_bool(F,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba))) ) ).

tff(fact_336_null__rec_I2_J,axiom,
    hBOOL(hAPP_l499746980t_bool(null_A791782855le_alt,nil_Ar557011903le_alt)) ).

tff(fact_337_List_Onull__def,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(null_A791782855le_alt,Xs_1))
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_338_eq__Nil__null,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( Xs_1 = nil_Ar557011903le_alt )
    <=> hBOOL(hAPP_l499746980t_bool(null_A791782855le_alt,Xs_1)) ) ).

tff(fact_339_null__rec_I1_J,axiom,
    ! [X_34: arrow_1893660431le_alt,Xs_48: list_A114658244le_alt] : ~ hBOOL(hAPP_l499746980t_bool(null_A791782855le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_34),Xs_48))) ).

tff(fact_340_Prof__def,axiom,
    arrow_5070731e_Prof = pi_Arr959578316t_bool(top_to788185952i_bool,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,arrow_1361987423le_Lin)) ).

tff(fact_341_lexord__cons__cons,axiom,
    ! [Aa: list_A114658244le_alt,X_2: list_l2028444773le_alt,Ba: list_A114658244le_alt,Y_2: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Aa),X_2)),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Ba),Y_2))),hAPP_f417980453t_bool(lexord616819815le_alt,R_2)))
    <=> ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),R_2))
        | ( ( Aa = Ba )
          & hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,X_2),Y_2)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2))) ) ) ) ).

tff(fact_342_lexord__cons__cons,axiom,
    ! [Aa: arrow_1893660431le_alt,X_2: list_A114658244le_alt,Ba: arrow_1893660431le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Aa),X_2)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Ba),Y_2))),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),R_2))
        | ( ( Aa = Ba )
          & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ) ) ).

tff(fact_343_distinct__butlast,axiom,
    ! [Xs_47: list_A114658244le_alt] :
      ( ( Xs_47 != nil_Ar557011903le_alt )
     => ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_47))
       => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_47))) ) ) ).

tff(fact_344_last_Osimps,axiom,
    ! [X_33: arrow_1893660431le_alt,Xs_46: list_A114658244le_alt] :
      ( ( ( Xs_46 = nil_Ar557011903le_alt )
       => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_33),Xs_46)) = X_33 ) )
      & ( ( Xs_46 != nil_Ar557011903le_alt )
       => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_33),Xs_46)) = last_A488133080le_alt(Xs_46) ) ) ) ).

tff(fact_345_top1I,axiom,
    ! [X_2: fun_fu2114379172t_bool] : hBOOL(hAPP_f1572141188l_bool(top_to827110112l_bool,X_2)) ).

tff(fact_346_top1I,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(top_to1312956197l_bool,X_2)) ).

tff(fact_347_top1I,axiom,
    ! [X_2: fun_Ar274636406t_bool] : hBOOL(hAPP_f995490902l_bool(top_to553140914l_bool,X_2)) ).

tff(fact_348_top1I,axiom,
    ! [X_2: produc472769767le_alt] : hBOOL(hAPP_P1178790471t_bool(top_to1138392227t_bool,X_2)) ).

tff(fact_349_top1I,axiom,
    ! [X_2: arrow_856714788e_indi] : hBOOL(hAPP_A997847300i_bool(top_to788185952i_bool,X_2)) ).

tff(fact_350_top1I,axiom,
    ! [X_2: arrow_1893660431le_alt] : hBOOL(hAPP_A1748732503t_bool(top_to814956427t_bool,X_2)) ).

tff(fact_351_Pi__UNIV,axiom,
    ! [A_1: fun_Pr2067565481t_bool] : ( pi_Pro1238944957t_bool(A_1,hAPP_f699791347l_bool(cOMBK_138598520le_alt,top_to1647826457l_bool)) = top_to1312956197l_bool ) ).

tff(fact_352_Pi__UNIV,axiom,
    ! [A_1: fun_fu3835832l_bool] : ( pi_fun1746584570t_bool(A_1,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,top_to1312956197l_bool)) = top_to827110112l_bool ) ).

tff(fact_353_Pi__UNIV,axiom,
    ! [A_1: fun_Ar1809396326i_bool] : ( pi_Arr959578316t_bool(A_1,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,top_to1312956197l_bool)) = top_to553140914l_bool ) ).

tff(fact_354_butlast_Osimps_I1_J,axiom,
    hAPP_l84111627le_alt(butlas1693249291le_alt,nil_Ar557011903le_alt) = nil_Ar557011903le_alt ).

tff(fact_355_lexord__Nil__right,axiom,
    ! [X_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),nil_Ar557011903le_alt)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ).

tff(fact_356_butlast_Osimps_I2_J,axiom,
    ! [X_32: arrow_1893660431le_alt,Xs_45: list_A114658244le_alt] :
      ( ( ( Xs_45 = nil_Ar557011903le_alt )
       => ( hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_32),Xs_45)) = nil_Ar557011903le_alt ) )
      & ( ( Xs_45 != nil_Ar557011903le_alt )
       => ( hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_32),Xs_45)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_32),hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_45)) ) ) ) ).

tff(fact_357_last__ConsL,axiom,
    ! [X_31: arrow_1893660431le_alt,Xs_44: list_A114658244le_alt] :
      ( ( Xs_44 = nil_Ar557011903le_alt )
     => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_31),Xs_44)) = X_31 ) ) ).

tff(fact_358_last__ConsR,axiom,
    ! [X_30: arrow_1893660431le_alt,Xs_43: list_A114658244le_alt] :
      ( ( Xs_43 != nil_Ar557011903le_alt )
     => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_30),Xs_43)) = last_A488133080le_alt(Xs_43) ) ) ).

tff(fact_359_lexord__Nil__left,axiom,
    ! [Y_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,nil_Ar557011903le_alt),Y_2)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
    <=> ? [A_7: arrow_1893660431le_alt,X_1: list_A114658244le_alt] : ( Y_2 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,A_7),X_1) ) ) ).

tff(fact_360_lexord__linear,axiom,
    ! [X_2: list_l2028444773le_alt,Y_2: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6)),R_2))
          | ( A_7 = B_6 )
          | hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,B_6),A_7)),R_2)) )
     => ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,X_2),Y_2)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2)))
        | ( X_2 = Y_2 )
        | hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Y_2),X_2)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2))) ) ) ).

tff(fact_361_lexord__linear,axiom,
    ! [X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),R_2))
          | ( A_7 = B_6 )
          | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,B_6),A_7)),R_2)) )
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
        | ( X_2 = Y_2 )
        | hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_2),X_2)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ) ).

tff(fact_362_lexord__irreflexive,axiom,
    ! [Xs_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( ! [X_1: list_A114658244le_alt] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),X_1)),R_2))
     => ~ hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Xs_1)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2))) ) ).

tff(fact_363_lexord__irreflexive,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] : ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),X_1)),R_2))
     => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Xs_1)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ).

tff(fact_364_iso__tuple__UNIV__I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).

tff(fact_365_iso__tuple__UNIV__I,axiom,
    ! [X_2: produc587761367le_alt] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),top_to1339422355t_bool)) ).

tff(fact_366_iso__tuple__UNIV__I,axiom,
    ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_367_iso__tuple__UNIV__I,axiom,
    ! [X_2: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),top_to788185952i_bool)) ).

tff(fact_368_iso__tuple__UNIV__I,axiom,
    ! [X_2: arrow_1893660431le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),top_to814956427t_bool)) ).

tff(fact_369_iso__tuple__UNIV__I,axiom,
    ! [X_2: produc472769767le_alt] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),top_to1138392227t_bool)) ).

tff(fact_370_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_Ar274636406t_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),top_to553140914l_bool)) ).

tff(fact_371_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),top_to1312956197l_bool)) ).

tff(fact_372_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_fu2114379172t_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),top_to827110112l_bool)) ).

tff(fact_373_UNIV__I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).

tff(fact_374_UNIV__I,axiom,
    ! [X_2: produc587761367le_alt] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),top_to1339422355t_bool)) ).

tff(fact_375_UNIV__I,axiom,
    ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_376_UNIV__I,axiom,
    ! [X_2: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),top_to788185952i_bool)) ).

tff(fact_377_UNIV__I,axiom,
    ! [X_2: arrow_1893660431le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),top_to814956427t_bool)) ).

tff(fact_378_UNIV__I,axiom,
    ! [X_2: produc472769767le_alt] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),top_to1138392227t_bool)) ).

tff(fact_379_UNIV__I,axiom,
    ! [X_2: fun_Ar274636406t_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),top_to553140914l_bool)) ).

tff(fact_380_UNIV__I,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),top_to1312956197l_bool)) ).

tff(fact_381_UNIV__I,axiom,
    ! [X_2: fun_fu2114379172t_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),top_to827110112l_bool)) ).

tff(fact_382_top__apply,axiom,
    ! [X_2: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f1572141188l_bool(top_to827110112l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_383_top__apply,axiom,
    ! [X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(top_to1312956197l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_384_top__apply,axiom,
    ! [X_2: fun_Ar274636406t_bool] :
      ( hBOOL(hAPP_f995490902l_bool(top_to553140914l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_385_top__apply,axiom,
    ! [X_2: produc472769767le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(top_to1138392227t_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_386_top__apply,axiom,
    ! [X_2: arrow_856714788e_indi] :
      ( hBOOL(hAPP_A997847300i_bool(top_to788185952i_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_387_top__apply,axiom,
    ! [X_2: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(top_to814956427t_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_388_takeWhile__not__last,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( Xs_1 != nil_Ar557011903le_alt )
     => ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1))
       => ( hAPP_l84111627le_alt(takeWh967109304le_alt(hAPP_f1592536333t_bool(hAPP_f2127477477t_bool(cOMBB_388242475le_alt,fNot),hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(cOMBC_1826973210t_bool,fequal1590852494le_alt),last_A488133080le_alt(Xs_1)))),Xs_1) = hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_1) ) ) ) ).

tff(fact_389_equal__Nil__null,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(equal_631514850le_alt,Xs_1),nil_Ar557011903le_alt))
    <=> hBOOL(hAPP_l499746980t_bool(null_A791782855le_alt,Xs_1)) ) ).

tff(fact_390_partition_Osimps_I1_J,axiom,
    ! [Pa: fun_Ar17477381t_bool] : ( partit758395576le_alt(Pa,nil_Ar557011903le_alt) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,nil_Ar557011903le_alt),nil_Ar557011903le_alt) ) ).

tff(fact_391_append__butlast__last__id,axiom,
    ! [Xs_42: list_A114658244le_alt] :
      ( ( Xs_42 != nil_Ar557011903le_alt )
     => ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_42)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,last_A488133080le_alt(Xs_42)),nil_Ar557011903le_alt)) = Xs_42 ) ) ).

tff(fact_392_takeWhile__tail,axiom,
    ! [Xs_1: list_A114658244le_alt,L_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt] :
      ( ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
     => ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),L_1))) = hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1) ) ) ).

tff(fact_393_append__eq__appendI,axiom,
    ! [Ys_18: list_A114658244le_alt,Us_2: list_A114658244le_alt,Xs_41: list_A114658244le_alt,Xs1_1: list_A114658244le_alt,Zs_4: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_41),Xs1_1) = Zs_4 )
     => ( ( Ys_18 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs1_1),Us_2) )
       => ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_41),Ys_18) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Zs_4),Us_2) ) ) ) ).

tff(fact_394_append__same__eq,axiom,
    ! [Ys_1: list_A114658244le_alt,Xs_1: list_A114658244le_alt,Zs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_1),Xs_1) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Zs_1),Xs_1) )
    <=> ( Ys_1 = Zs_1 ) ) ).

tff(fact_395_same__append__eq,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,Zs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Zs_1) )
    <=> ( Ys_1 = Zs_1 ) ) ).

tff(fact_396_append__eq__append__conv2,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,Zs_1: list_A114658244le_alt,Ts: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Zs_1),Ts) )
    <=> ? [Us: list_A114658244le_alt] :
          ( ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Zs_1),Us) )
            & ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Us),Ys_1) = Ts ) )
          | ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Us) = Zs_1 )
            & ( Ys_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Us),Ts) ) ) ) ) ).

tff(fact_397_append__assoc,axiom,
    ! [Xs_40: list_A114658244le_alt,Ys_17: list_A114658244le_alt,Zs_3: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_40),Ys_17)),Zs_3) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_40),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_17),Zs_3)) ) ).

tff(fact_398_equal__list__def,axiom,
    ! [X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(equal_631514850le_alt,X_2),Y_2))
    <=> ( X_2 = Y_2 ) ) ).

tff(fact_399_append__Cons,axiom,
    ! [X_29: arrow_1893660431le_alt,Xs_39: list_A114658244le_alt,Ys_16: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_29),Xs_39)),Ys_16) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_29),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_39),Ys_16)) ) ).

tff(fact_400_Cons__eq__appendI,axiom,
    ! [Xs_38: list_A114658244le_alt,Zs_2: list_A114658244le_alt,X_28: arrow_1893660431le_alt,Xs1: list_A114658244le_alt,Ys_15: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_28),Xs1) = Ys_15 )
     => ( ( Xs_38 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs1),Zs_2) )
       => ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_28),Xs_38) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_15),Zs_2) ) ) ) ).

tff(fact_401_append__Nil,axiom,
    ! [Ys_14: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,nil_Ar557011903le_alt),Ys_14) = Ys_14 ) ).

tff(fact_402_Nil__is__append__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( nil_Ar557011903le_alt = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) )
    <=> ( ( Xs_1 = nil_Ar557011903le_alt )
        & ( Ys_1 = nil_Ar557011903le_alt ) ) ) ).

tff(fact_403_append__Nil2,axiom,
    ! [Xs_37: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_37),nil_Ar557011903le_alt) = Xs_37 ) ).

tff(fact_404_self__append__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) )
    <=> ( Ys_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_405_self__append__conv2,axiom,
    ! [Ys_1: list_A114658244le_alt,Xs_1: list_A114658244le_alt] :
      ( ( Ys_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) )
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_406_append__is__Nil__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) = nil_Ar557011903le_alt )
    <=> ( ( Xs_1 = nil_Ar557011903le_alt )
        & ( Ys_1 = nil_Ar557011903le_alt ) ) ) ).

tff(fact_407_append__self__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) = Xs_1 )
    <=> ( Ys_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_408_append__self__conv2,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1) = Ys_1 )
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_409_eq__Nil__appendI,axiom,
    ! [Xs_36: list_A114658244le_alt,Ys_13: list_A114658244le_alt] :
      ( ( Xs_36 = Ys_13 )
     => ( Xs_36 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,nil_Ar557011903le_alt),Ys_13) ) ) ).

tff(fact_410_takeWhile_Osimps_I1_J,axiom,
    ! [Pa: fun_Ar17477381t_bool] : ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),nil_Ar557011903le_alt) = nil_Ar557011903le_alt ) ).

tff(fact_411_distinct__takeWhile,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1))
     => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1))) ) ).

tff(fact_412_append__eq__Cons__conv,axiom,
    ! [Ys_1: list_A114658244le_alt,Zs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_1),Zs_1) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) )
    <=> ( ( ( Ys_1 = nil_Ar557011903le_alt )
          & ( Zs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) ) )
        | ? [Ys_12: list_A114658244le_alt] :
            ( ( Ys_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Ys_12) )
            & ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_12),Zs_1) = Xs_1 ) ) ) ) ).

tff(fact_413_Cons__eq__append__conv,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,Zs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_1),Zs_1) )
    <=> ( ( ( Ys_1 = nil_Ar557011903le_alt )
          & ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) = Zs_1 ) )
        | ? [Ys_12: list_A114658244le_alt] :
            ( ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Ys_12) = Ys_1 )
            & ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_12),Zs_1) ) ) ) ) ).

tff(fact_414_append1__eq__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),nil_Ar557011903le_alt)) )
    <=> ( ( Xs_1 = Ys_1 )
        & ( X_2 = Y_2 ) ) ) ).

tff(fact_415_butlast__append,axiom,
    ! [Xs_35: list_A114658244le_alt,Ys_11: list_A114658244le_alt] :
      ( ( ( Ys_11 = nil_Ar557011903le_alt )
       => ( hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_35),Ys_11)) = hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_35) ) )
      & ( ( Ys_11 != nil_Ar557011903le_alt )
       => ( hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_35),Ys_11)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_35),hAPP_l84111627le_alt(butlas1693249291le_alt,Ys_11)) ) ) ) ).

tff(fact_416_last__appendL,axiom,
    ! [Xs_34: list_A114658244le_alt,Ys_10: list_A114658244le_alt] :
      ( ( Ys_10 = nil_Ar557011903le_alt )
     => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_34),Ys_10)) = last_A488133080le_alt(Xs_34) ) ) ).

tff(fact_417_last__appendR,axiom,
    ! [Xs_33: list_A114658244le_alt,Ys_9: list_A114658244le_alt] :
      ( ( Ys_9 != nil_Ar557011903le_alt )
     => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_33),Ys_9)) = last_A488133080le_alt(Ys_9) ) ) ).

tff(fact_418_last__append,axiom,
    ! [Xs_32: list_A114658244le_alt,Ys_8: list_A114658244le_alt] :
      ( ( ( Ys_8 = nil_Ar557011903le_alt )
       => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_32),Ys_8)) = last_A488133080le_alt(Xs_32) ) )
      & ( ( Ys_8 != nil_Ar557011903le_alt )
       => ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_32),Ys_8)) = last_A488133080le_alt(Ys_8) ) ) ) ).

tff(fact_419_lexord__append__leftI,axiom,
    ! [X_2: list_A114658244le_alt,U: list_A114658244le_alt,V: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,U),V)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X_2),U)),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X_2),V))),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ).

tff(fact_420_takeWhile_Osimps_I2_J,axiom,
    ! [Xs_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt] :
      ( ( hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
       => ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1)) ) )
      & ( ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
       => ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = nil_Ar557011903le_alt ) ) ) ).

tff(fact_421_maps__simps_I1_J,axiom,
    ! [F: fun_Ar849108972le_alt,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(maps_A652163713le_alt(F),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_A1382181054le_alt(F,X_2)),hAPP_l84111627le_alt(maps_A652163713le_alt(F),Xs_1)) ) ).

tff(fact_422_butlast__snoc,axiom,
    ! [Xs_31: list_A114658244le_alt,X_27: arrow_1893660431le_alt] : ( hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_31),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_27),nil_Ar557011903le_alt))) = Xs_31 ) ).

tff(fact_423_last__snoc,axiom,
    ! [Xs_30: list_A114658244le_alt,X_26: arrow_1893660431le_alt] : ( last_A488133080le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_30),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_26),nil_Ar557011903le_alt))) = X_26 ) ).

tff(fact_424_UNIV__def,axiom,
    top_top_fun_nat_bool = collect_nat(hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)) ).

tff(fact_425_UNIV__def,axiom,
    top_to827110112l_bool = collec71394895t_bool(hAPP_b1777246598l_bool(cOMBK_1279003709t_bool,fTrue)) ).

tff(fact_426_UNIV__def,axiom,
    top_to553140914l_bool = collec1236161569t_bool(hAPP_b1078573912l_bool(cOMBK_445086735t_bool,fTrue)) ).

tff(fact_427_UNIV__def,axiom,
    top_to1138392227t_bool = collec1988958098le_alt(hAPP_b128655177t_bool(cOMBK_198697344le_alt,fTrue)) ).

tff(fact_428_UNIV__def,axiom,
    top_to788185952i_bool = collec1597001935e_indi(hAPP_b549570054i_bool(cOMBK_561380029e_indi,fTrue)) ).

tff(fact_429_UNIV__def,axiom,
    top_to814956427t_bool = collec12892580le_alt(hAPP_b916665189t_bool(cOMBK_2077209654le_alt,fTrue)) ).

tff(fact_430_UNIV__def,axiom,
    top_to1312956197l_bool = collec2125531966t_bool(hAPP_b1272691967l_bool(cOMBK_81143760t_bool,fTrue)) ).

tff(fact_431_lexord__append__left__rightI,axiom,
    ! [U: list_l2028444773le_alt,X_2: list_l2028444773le_alt,Y_2: list_l2028444773le_alt,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),R_2))
     => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,U),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Aa),X_2))),hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,U),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Ba),Y_2)))),hAPP_f417980453t_bool(lexord616819815le_alt,R_2))) ) ).

tff(fact_432_lexord__append__left__rightI,axiom,
    ! [U: list_A114658244le_alt,X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),R_2))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,U),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Aa),X_2))),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,U),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Ba),Y_2)))),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ).

tff(fact_433_snoc__eq__iff__butlast,axiom,
    ! [Xs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt)) = Ys_1 )
    <=> ( ( Ys_1 != nil_Ar557011903le_alt )
        & ( hAPP_l84111627le_alt(butlas1693249291le_alt,Ys_1) = Xs_1 )
        & ( last_A488133080le_alt(Ys_1) = X_2 ) ) ) ).

tff(fact_434_lexord__append__rightI,axiom,
    ! [X_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool,Y_2: list_A114658244le_alt] :
      ( ? [B_6: arrow_1893660431le_alt,Z_4: list_A114658244le_alt] : ( Y_2 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,B_6),Z_4) )
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X_2),Y_2))),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ).

tff(fact_435_lexord__append__leftD,axiom,
    ! [X_2: list_l2028444773le_alt,U: list_l2028444773le_alt,V: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,X_2),U)),hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,X_2),V))),hAPP_f417980453t_bool(lexord616819815le_alt,R_2)))
     => ( ! [A_7: list_A114658244le_alt] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),A_7)),R_2))
       => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,U),V)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2))) ) ) ).

tff(fact_436_lexord__append__leftD,axiom,
    ! [X_2: list_A114658244le_alt,U: list_A114658244le_alt,V: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X_2),U)),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X_2),V))),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
     => ( ! [A_7: arrow_1893660431le_alt] : ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),A_7)),R_2))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,U),V)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ) ).

tff(fact_437_rev__induct,axiom,
    ! [Xs_1: list_A114658244le_alt,Pa: fun_li1109619974t_bool] :
      ( hBOOL(hAPP_l499746980t_bool(Pa,nil_Ar557011903le_alt))
     => ( ! [X_1: arrow_1893660431le_alt,Xs_17: list_A114658244le_alt] :
            ( hBOOL(hAPP_l499746980t_bool(Pa,Xs_17))
           => hBOOL(hAPP_l499746980t_bool(Pa,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_17),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),nil_Ar557011903le_alt)))) )
       => hBOOL(hAPP_l499746980t_bool(Pa,Xs_1)) ) ) ).

tff(fact_438_rev__cases,axiom,
    ! [Xs_29: list_A114658244le_alt] :
      ( ( Xs_29 != nil_Ar557011903le_alt )
     => ~ ! [Ys: list_A114658244le_alt,Y_9: arrow_1893660431le_alt] : ( Xs_29 != hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),nil_Ar557011903le_alt)) ) ) ).

tff(fact_439_snoc__listrel1__snoc__iff,axiom,
    ! [Xs_1: list_l2028444773le_alt,X_2: list_A114658244le_alt,Ys_1: list_l2028444773le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,Xs_1),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),nil_li2054189844le_alt))),hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,Ys_1),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),nil_li2054189844le_alt)))),hAPP_f417980453t_bool(listre767458683le_alt,R_2)))
    <=> ( ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(listre767458683le_alt,R_2)))
          & ( X_2 = Y_2 ) )
        | ( ( Xs_1 = Ys_1 )
          & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_2)) ) ) ) ).

tff(fact_440_snoc__listrel1__snoc__iff,axiom,
    ! [Xs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt))),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),nil_Ar557011903le_alt)))),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
    <=> ( ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
          & ( X_2 = Y_2 ) )
        | ( ( Xs_1 = Ys_1 )
          & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_2)) ) ) ) ).

tff(fact_441_rotate1__def,axiom,
    ! [Xs_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(rotate1753650700le_alt,Xs_1) = hAPP_l84111627le_alt(list_c1024366775le_alt(nil_Ar557011903le_alt,hAPP_f218129964le_alt(hAPP_f757086845le_alt(cOMBB_1076781858le_alt,hAPP_f204005175le_alt(cOMBC_1833749623le_alt,append1597383892le_alt)),hAPP_l1822938419le_alt(hAPP_f274624079le_alt(cOMBC_673369480le_alt,cons_A1647044463le_alt),nil_Ar557011903le_alt))),Xs_1) ) ).

tff(fact_442_rotate__simps,axiom,
    ! [X_25: arrow_1893660431le_alt,Xs_28: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(rotate1753650700le_alt,nil_Ar557011903le_alt) = nil_Ar557011903le_alt )
      & ( hAPP_l84111627le_alt(rotate1753650700le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_25),Xs_28)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_28),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_25),nil_Ar557011903le_alt)) ) ) ).

tff(fact_443_UNIV__witness,axiom,
    ? [X_1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),top_top_fun_nat_bool)) ).

tff(fact_444_UNIV__witness,axiom,
    ? [X_1: produc587761367le_alt] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),top_to1339422355t_bool)) ).

tff(fact_445_UNIV__witness,axiom,
    ? [X_1: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool)) ).

tff(fact_446_UNIV__witness,axiom,
    ? [X_1: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),top_to788185952i_bool)) ).

tff(fact_447_UNIV__witness,axiom,
    ? [X_1: arrow_1893660431le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),top_to814956427t_bool)) ).

tff(fact_448_UNIV__witness,axiom,
    ? [X_1: produc472769767le_alt] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),top_to1138392227t_bool)) ).

tff(fact_449_UNIV__witness,axiom,
    ? [X_1: fun_Ar274636406t_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),top_to553140914l_bool)) ).

tff(fact_450_UNIV__witness,axiom,
    ? [X_1: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),top_to1312956197l_bool)) ).

tff(fact_451_UNIV__witness,axiom,
    ? [X_1: fun_fu2114379172t_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),top_to827110112l_bool)) ).

tff(fact_452_UNIV__eq__I,axiom,
    ! [A_1: fun_nat_bool] :
      ( ! [X_1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
     => ( top_top_fun_nat_bool = A_1 ) ) ).

tff(fact_453_UNIV__eq__I,axiom,
    ! [A_1: fun_Pr486337689t_bool] :
      ( ! [X_1: produc587761367le_alt] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),A_1))
     => ( top_to1339422355t_bool = A_1 ) ) ).

tff(fact_454_UNIV__eq__I,axiom,
    ! [A_1: fun_bool_bool] :
      ( ! [X_1: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
     => ( top_to1647826457l_bool = A_1 ) ) ).

tff(fact_455_UNIV__eq__I,axiom,
    ! [A_1: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A_1))
     => ( top_to788185952i_bool = A_1 ) ) ).

tff(fact_456_UNIV__eq__I,axiom,
    ! [A_1: fun_Ar17477381t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),A_1))
     => ( top_to814956427t_bool = A_1 ) ) ).

tff(fact_457_UNIV__eq__I,axiom,
    ! [A_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A_1))
     => ( top_to1138392227t_bool = A_1 ) ) ).

tff(fact_458_UNIV__eq__I,axiom,
    ! [A_1: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A_1))
     => ( top_to553140914l_bool = A_1 ) ) ).

tff(fact_459_UNIV__eq__I,axiom,
    ! [A_1: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A_1))
     => ( top_to1312956197l_bool = A_1 ) ) ).

tff(fact_460_UNIV__eq__I,axiom,
    ! [A_1: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A_1))
     => ( top_to827110112l_bool = A_1 ) ) ).

tff(fact_461_rotate1__is__Nil__conv,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(rotate1753650700le_alt,Xs_1) = nil_Ar557011903le_alt )
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_462_distinct1__rotate,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(rotate1753650700le_alt,Xs_1)))
    <=> hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1)) ) ).

tff(fact_463_listrel1I2,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Ys_1))),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ).

tff(fact_464_not__listrel1__Nil,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),nil_Ar557011903le_alt)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ).

tff(fact_465_not__Nil__listrel1,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,nil_Ar557011903le_alt),Xs_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ).

tff(fact_466_append__listrel1I,axiom,
    ! [Us_1: list_A114658244le_alt,Vs_1: list_A114658244le_alt,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( ( ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
          & ( Us_1 = Vs_1 ) )
        | ( ( Xs_1 = Ys_1 )
          & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Us_1),Vs_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) )
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Us_1)),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys_1),Vs_1))),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ).

tff(fact_467_Cons__listrel1__Cons,axiom,
    ! [X_2: list_A114658244le_alt,Xs_1: list_l2028444773le_alt,Y_2: list_A114658244le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Xs_1)),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1))),hAPP_f417980453t_bool(listre767458683le_alt,R_2)))
    <=> ( ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_2))
          & ( Xs_1 = Ys_1 ) )
        | ( ( X_2 = Y_2 )
          & hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(listre767458683le_alt,R_2))) ) ) ) ).

tff(fact_468_Cons__listrel1__Cons,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
    <=> ( ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_2))
          & ( Xs_1 = Ys_1 ) )
        | ( ( X_2 = Y_2 )
          & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ) ) ).

tff(fact_469_listrel1I1,axiom,
    ! [Xs_1: list_l2028444773le_alt,X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_2))
     => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Xs_1)),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Xs_1))),hAPP_f417980453t_bool(listre767458683le_alt,R_2))) ) ).

tff(fact_470_listrel1I1,axiom,
    ! [Xs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_2))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Xs_1))),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ).

tff(fact_471_listrel1I,axiom,
    ! [Ys_1: list_l2028444773le_alt,Xs_1: list_l2028444773le_alt,Us_1: list_l2028444773le_alt,Vs_1: list_l2028444773le_alt,X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_2))
     => ( ( Xs_1 = hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,Us_1),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Vs_1)) )
       => ( ( Ys_1 = hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,Us_1),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Vs_1)) )
         => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(listre767458683le_alt,R_2))) ) ) ) ).

tff(fact_472_listrel1I,axiom,
    ! [Ys_1: list_A114658244le_alt,Xs_1: list_A114658244le_alt,Us_1: list_A114658244le_alt,Vs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_2))
     => ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Us_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Vs_1)) )
       => ( ( Ys_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Us_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Vs_1)) )
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ) ) ).

tff(fact_473_listrel1E,axiom,
    ! [Xs_1: list_l2028444773le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(listre767458683le_alt,R_2)))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9)),R_2))
           => ! [Us: list_l2028444773le_alt,Vs: list_l2028444773le_alt] :
                ( ( Xs_1 = hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,Us),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_1),Vs)) )
               => ( Ys_1 != hAPP_l1913469717le_alt(hAPP_l2145422509le_alt(append1312904639le_alt,Us),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_9),Vs)) ) ) ) ) ).

tff(fact_474_listrel1E,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9)),R_2))
           => ! [Us: list_A114658244le_alt,Vs: list_A114658244le_alt] :
                ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Us),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Vs)) )
               => ( Ys_1 != hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Us),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Vs)) ) ) ) ) ).

tff(fact_475_Cons__listrel1E1,axiom,
    ! [X_2: list_A114658244le_alt,Xs_1: list_l2028444773le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Xs_1)),Ys_1)),hAPP_f417980453t_bool(listre767458683le_alt,R_2)))
     => ( ! [Y_9: list_A114658244le_alt] :
            ( ( Ys_1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_9),Xs_1) )
           => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_9)),R_2)) )
       => ~ ! [Zs: list_l2028444773le_alt] :
              ( ( Ys_1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Zs) )
             => ~ hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Zs)),hAPP_f417980453t_bool(listre767458683le_alt,R_2))) ) ) ) ).

tff(fact_476_Cons__listrel1E1,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
     => ( ! [Y_9: arrow_1893660431le_alt] :
            ( ( Ys_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Xs_1) )
           => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_9)),R_2)) )
       => ~ ! [Zs: list_A114658244le_alt] :
              ( ( Ys_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs) )
             => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Zs)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ) ) ).

tff(fact_477_Cons__listrel1E2,axiom,
    ! [Xs_1: list_l2028444773le_alt,Y_2: list_A114658244le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1))),hAPP_f417980453t_bool(listre767458683le_alt,R_2)))
     => ( ! [X_1: list_A114658244le_alt] :
            ( ( Xs_1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_1),Ys_1) )
           => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_2)),R_2)) )
       => ~ ! [Zs: list_l2028444773le_alt] :
              ( ( Xs_1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Zs) )
             => ~ hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Zs),Ys_1)),hAPP_f417980453t_bool(listre767458683le_alt,R_2))) ) ) ) ).

tff(fact_478_Cons__listrel1E2,axiom,
    ! [Xs_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
     => ( ! [X_1: arrow_1893660431le_alt] :
            ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Ys_1) )
           => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_2)),R_2)) )
       => ~ ! [Zs: list_A114658244le_alt] :
              ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Zs) )
             => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Zs),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2))) ) ) ) ).

tff(fact_479_Lin__def,axiom,
    arrow_1361987423le_Lin = collec2125531966t_bool(order_1266734903le_alt(top_to814956427t_bool)) ).

tff(fact_480_dropWhile__eq__Cons__conv,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1) )
    <=> ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1)) )
        & ~ hBOOL(hAPP_A1748732503t_bool(Pa,Y_2)) ) ) ).

tff(fact_481_Nil2__notin__lex,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),nil_Ar557011903le_alt)),hAPP_f369701637t_bool(lex_Ar686335011le_alt,R_2))) ).

tff(fact_482_Nil__notin__lex,axiom,
    ! [Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] : ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,nil_Ar557011903le_alt),Ys_1)),hAPP_f369701637t_bool(lex_Ar686335011le_alt,R_2))) ).

tff(fact_483_partition_Osimps_I2_J,axiom,
    ! [Pa: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] : ( partit758395576le_alt(Pa,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,hAPP_f6098781le_alt(hAPP_f423920914le_alt(cOMBS_917035857le_alt,hAPP_f1967789246le_alt(hAPP_f752890973le_alt(cOMBB_1206549317le_alt,cOMBS_19686701le_alt),hAPP_f1455388473le_alt(hAPP_f1097645385le_alt(cOMBB_1772667958le_alt,hAPP_f1372126793le_alt(cOMBB_730268484le_alt,if_Pro1687484775le_alt(hAPP_A1748732503t_bool(Pa,X_2)))),hAPP_f1274386949le_alt(hAPP_f1142066787le_alt(cOMBB_1071360260le_alt,produc1742925389le_alt),hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2))))),hAPP_f1274386949le_alt(hAPP_f905689843le_alt(cOMBC_1284478484le_alt,hAPP_f1148079597le_alt(hAPP_f1250095511le_alt(cOMBB_1247716816le_alt,cOMBB_250395785le_alt),produc1742925389le_alt)),hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2)))),partit758395576le_alt(Pa,Xs_1)) ) ).

tff(fact_484_split__weak__cong,axiom,
    ! [Ca: fun_Ar331856045t_bool,P_1: produc472769767le_alt,Q_2: produc472769767le_alt] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,Ca),P_1))
      <=> hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,Ca),Q_2)) ) ) ).

tff(fact_485_split__weak__cong,axiom,
    ! [Ca: fun_li380014893le_alt,P_1: produc587761367le_alt,Q_2: produc587761367le_alt] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,Ca),P_1) = hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,Ca),Q_2) ) ) ).

tff(fact_486_prod_Osimps_I2_J,axiom,
    ! [F1: fun_li380014893le_alt,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] : ( hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,F1),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(F1,Aa),Ba) ) ).

tff(fact_487_prod_Osimps_I2_J,axiom,
    ! [F1: fun_Ar331856045t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F1),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))
    <=> hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F1,Aa),Ba)) ) ).

tff(fact_488_split__conv,axiom,
    ! [F: fun_li380014893le_alt,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] : ( hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,F),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(F,Aa),Ba) ) ).

tff(fact_489_split__conv,axiom,
    ! [F: fun_Ar331856045t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))
    <=> hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F,Aa),Ba)) ) ).

tff(fact_490_dropWhile_Osimps_I2_J,axiom,
    ! [Xs_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt] :
      ( ( hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
       => ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1) ) )
      & ( ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
       => ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) ) ) ) ).

tff(fact_491_dropWhile_Osimps_I1_J,axiom,
    ! [Pa: fun_Ar17477381t_bool] : ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),nil_Ar557011903le_alt) = nil_Ar557011903le_alt ) ).

tff(fact_492_distinct__dropWhile,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1))
     => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1))) ) ).

tff(fact_493_split__eta,axiom,
    ! [F: fun_Pr1186243091le_alt] : ( hAPP_f1221439459le_alt(produc2052829583le_alt,hAPP_f6098781le_alt(hAPP_f533347863le_alt(cOMBB_1792551872le_alt,hAPP_f635935679le_alt(cOMBB_1945714076le_alt,F)),produc1742925389le_alt)) = F ) ).

tff(fact_494_split__eta,axiom,
    ! [F: fun_Pr2067565481t_bool] : ( hAPP_f782115833t_bool(produc73018783t_bool,hAPP_f783327207t_bool(hAPP_f404316901t_bool(cOMBB_1598772817le_alt,hAPP_f1124798181t_bool(cOMBB_2030766369le_alt,F)),produc1590937303le_alt)) = F ) ).

tff(fact_495_split__curry,axiom,
    ! [F: fun_Pr2067565481t_bool] : ( hAPP_f782115833t_bool(produc73018783t_bool,produc410835390t_bool(F)) = F ) ).

tff(fact_496_split__curry,axiom,
    ! [F: fun_Pr1186243091le_alt] : ( hAPP_f1221439459le_alt(produc2052829583le_alt,produc1639868974le_alt(F)) = F ) ).

tff(fact_497_curry__split,axiom,
    ! [F: fun_Ar331856045t_bool] : ( produc410835390t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F)) = F ) ).

tff(fact_498_curry__split,axiom,
    ! [F: fun_li380014893le_alt] : ( produc1639868974le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,F)) = F ) ).

tff(fact_499_internal__split__def,axiom,
    produc2015632596t_bool = produc73018783t_bool ).

tff(fact_500_internal__split__def,axiom,
    produc1354545732le_alt = produc2052829583le_alt ).

tff(fact_501_takeWhile__dropWhile__id,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1)),hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1)) = Xs_1 ) ).

tff(fact_502_cond__split__eta,axiom,
    ! [F: fun_li380014893le_alt,G: fun_Pr1186243091le_alt] :
      ( ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] : ( hAPP_l1580775710le_alt(hAPP_l660415097le_alt(F,X_1),Y_9) = hAPP_P205052337le_alt(G,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9)) )
     => ( hAPP_f1221439459le_alt(produc2052829583le_alt,F) = G ) ) ).

tff(fact_503_cond__split__eta,axiom,
    ! [G: fun_Pr2067565481t_bool,F: fun_Ar331856045t_bool] :
      ( ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F,X_1),Y_9))
        <=> hBOOL(hAPP_P1178790471t_bool(G,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9))) )
     => ( hAPP_f782115833t_bool(produc73018783t_bool,F) = G ) ) ).

tff(fact_504_splitE2,axiom,
    ! [Q_1: fun_Pr486337689t_bool,Pa: fun_li380014893le_alt,Z_3: produc587761367le_alt] :
      ( hBOOL(hAPP_P1894408759t_bool(Q_1,hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,Pa),Z_3)))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( ( Z_3 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_P1894408759t_bool(Q_1,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(Pa,X_1),Y_9))) ) ) ).

tff(fact_505_splitE2,axiom,
    ! [Q_1: fun_bool_bool,Pa: fun_Ar331856045t_bool,Z_3: produc472769767le_alt] :
      ( hBOOL(hAPP_bool_bool(Q_1,hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,Pa),Z_3)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( Z_3 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,X_1),Y_9))) ) ) ).

tff(fact_506_split__cong,axiom,
    ! [P_1: produc587761367le_alt,F: fun_li380014893le_alt,G: fun_li380014893le_alt,Q_2: produc587761367le_alt] :
      ( ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
          ( ( hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) = Q_2 )
         => ( hAPP_l1580775710le_alt(hAPP_l660415097le_alt(F,X_1),Y_9) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(G,X_1),Y_9) ) )
     => ( ( P_1 = Q_2 )
       => ( hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,F),P_1) = hAPP_P205052337le_alt(hAPP_f1221439459le_alt(produc2052829583le_alt,G),Q_2) ) ) ) ).

tff(fact_507_split__cong,axiom,
    ! [P_1: produc472769767le_alt,G: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool,Q_2: produc472769767le_alt] :
      ( ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
          ( ( hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) = Q_2 )
         => ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F,X_1),Y_9))
          <=> hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(G,X_1),Y_9)) ) )
     => ( ( P_1 = Q_2 )
       => ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F),P_1))
        <=> hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,G),Q_2)) ) ) ) ).

tff(fact_508_Cons__in__lex,axiom,
    ! [X_2: list_A114658244le_alt,Xs_1: list_l2028444773le_alt,Y_2: list_A114658244le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Xs_1)),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1))),hAPP_f417980453t_bool(lex_li810040752le_alt,R_2)))
    <=> ( ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_2))
          & ( hAPP_l1496043450lt_nat(size_s317648763le_alt,Xs_1) = hAPP_l1496043450lt_nat(size_s317648763le_alt,Ys_1) ) )
        | ( ( X_2 = Y_2 )
          & hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(lex_li810040752le_alt,R_2))) ) ) ) ).

tff(fact_509_Cons__in__lex,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))),hAPP_f369701637t_bool(lex_Ar686335011le_alt,R_2)))
    <=> ( ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_2))
          & ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_1) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys_1) ) )
        | ( ( X_2 = Y_2 )
          & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(lex_Ar686335011le_alt,R_2))) ) ) ) ).

tff(fact_510_not__distinct__decomp,axiom,
    ! [Ws: list_A114658244le_alt] :
      ( ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Ws))
     => ? [Xs_17: list_A114658244le_alt,Ys: list_A114658244le_alt,Zs: list_A114658244le_alt,Y_9: arrow_1893660431le_alt] : ( Ws = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_17),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),nil_Ar557011903le_alt)),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),nil_Ar557011903le_alt)),Zs)))) ) ) ).

tff(fact_511_listrel_OCons,axiom,
    ! [Xs_1: list_l2028444773le_alt,Ys_1: list_l2028444773le_alt,X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),R_2))
     => ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(listre770069484le_alt,R_2)))
       => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Xs_1)),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1))),hAPP_f417980453t_bool(listre770069484le_alt,R_2))) ) ) ).

tff(fact_512_listrel_OCons,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),R_2))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))),hAPP_f369701637t_bool(listre1191473383le_alt,R_2))) ) ) ).

tff(fact_513_tl__append,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(tl_Arr1883752598le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1)) = hAPP_l84111627le_alt(list_c1024366775le_alt(hAPP_l84111627le_alt(tl_Arr1883752598le_alt,Ys_1),hAPP_f688183683le_alt(cOMBK_930998768le_alt,hAPP_l86320102le_alt(hAPP_f204005175le_alt(cOMBC_1833749623le_alt,append1597383892le_alt),Ys_1))),Xs_1) ) ).

tff(fact_514_equal,axiom,
    equal_631514850le_alt = fequal928191109le_alt ).

tff(fact_515_splitI,axiom,
    ! [F: fun_li495175091t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(F,Aa),Ba))
     => hBOOL(hAPP_P1894408759t_bool(hAPP_f1732069219t_bool(produc631952405t_bool,F),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba))) ) ).

tff(fact_516_splitI,axiom,
    ! [F: fun_Ar331856045t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F,Aa),Ba))
     => hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba))) ) ).

tff(fact_517_prod__caseI,axiom,
    ! [F1: fun_li495175091t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(F1,Aa),Ba))
     => hBOOL(hAPP_P1894408759t_bool(hAPP_f1732069219t_bool(produc631952405t_bool,F1),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba))) ) ).

tff(fact_518_prod__caseI,axiom,
    ! [F1: fun_Ar331856045t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F1,Aa),Ba))
     => hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F1),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba))) ) ).

tff(fact_519_mem__splitI,axiom,
    ! [Z_3: nat,Ca: fun_Ar113775056t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_A75605626t_bool(hAPP_A98481698t_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_P1123315306t_bool(hAPP_f2044004281t_bool(produc802256322t_bool,Ca),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))) ) ).

tff(fact_520_mem__splitI,axiom,
    ! [Z_3: produc587761367le_alt,Ca: fun_Ar26892405t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Z_3),hAPP_A876841247t_bool(hAPP_A837018253t_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Z_3),hAPP_P588680495t_bool(hAPP_f582323651t_bool(produc2013750231t_bool,Ca),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))) ) ).

tff(fact_521_mem__splitI,axiom,
    ! [Z_3: arrow_1893660431le_alt,Ca: fun_Ar1044946517t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Z_3),hAPP_A2063800319t_bool(hAPP_A1975288231t_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Z_3),hAPP_P1328248815t_bool(hAPP_f919250425t_bool(produc542980935t_bool,Ca),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))) ) ).

tff(fact_522_mem__splitI,axiom,
    ! [Z_3: arrow_856714788e_indi,Ca: fun_Ar1628482114i_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Z_3),hAPP_A1492453356i_bool(hAPP_A891807578i_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Z_3),hAPP_P1859429372i_bool(hAPP_f1028383325i_bool(produc762033828i_bool,Ca),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))) ) ).

tff(fact_523_mem__splitI,axiom,
    ! [Z_3: bool,Ca: fun_Ar949229051l_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_A463015077l_bool(hAPP_A1316408339l_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_P1103642805l_bool(hAPP_f874384847l_bool(produc327487325l_bool,Ca),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))) ) ).

tff(fact_524_mem__splitI,axiom,
    ! [Z_3: produc472769767le_alt,Ca: fun_li1684108543t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Z_3),hAPP_l1875392034t_bool(hAPP_l1232500765t_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Z_3),hAPP_P1708597583t_bool(hAPP_f1879310829t_bool(produc47507185t_bool,Ca),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)))) ) ).

tff(fact_525_mem__splitI,axiom,
    ! [Z_3: fun_Ar274636406t_bool,Ca: fun_li1290371598l_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Z_3),hAPP_l1144124209l_bool(hAPP_l362966444l_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Z_3),hAPP_P878768990l_bool(hAPP_f1371571723l_bool(produc632580864l_bool,Ca),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)))) ) ).

tff(fact_526_mem__splitI,axiom,
    ! [Z_3: fun_Pr2067565481t_bool,Ca: fun_li1959074549l_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Z_3),hAPP_l1876389606l_bool(hAPP_l328381505l_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Z_3),hAPP_P171164537l_bool(hAPP_f229317091l_bool(produc999826263l_bool,Ca),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)))) ) ).

tff(fact_527_mem__splitI,axiom,
    ! [Z_3: fun_fu2114379172t_bool,Ca: fun_li123689532l_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Z_3),hAPP_l592144991l_bool(hAPP_l830471642l_bool(Ca,Aa),Ba)))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Z_3),hAPP_P1986703244l_bool(hAPP_f928402023l_bool(produc1727510830l_bool,Ca),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)))) ) ).

tff(fact_528_listrel__Nil2,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),nil_Ar557011903le_alt)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
     => ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_529_listrel__Nil1,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,nil_Ar557011903le_alt),Xs_1)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
     => ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_530_neq__if__length__neq,axiom,
    ! [Xs_27: list_A114658244le_alt,Ys_7: list_A114658244le_alt] :
      ( ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_27) != hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys_7) )
     => ( Xs_27 != Ys_7 ) ) ).

tff(fact_531_listrel__eq__len,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
     => ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_1) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys_1) ) ) ).

tff(fact_532_splitD,axiom,
    ! [F: fun_li495175091t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt] :
      ( hBOOL(hAPP_P1894408759t_bool(hAPP_f1732069219t_bool(produc631952405t_bool,F),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)))
     => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(F,Aa),Ba)) ) ).

tff(fact_533_splitD,axiom,
    ! [F: fun_Ar331856045t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,F),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)))
     => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(F,Aa),Ba)) ) ).

tff(fact_534_length__rotate1,axiom,
    ! [Xs_26: list_A114658244le_alt] : ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,hAPP_l84111627le_alt(rotate1753650700le_alt,Xs_26)) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_26) ) ).

tff(fact_535_tl_Osimps_I2_J,axiom,
    ! [X_24: arrow_1893660431le_alt,Xs_25: list_A114658244le_alt] : ( hAPP_l84111627le_alt(tl_Arr1883752598le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_24),Xs_25)) = Xs_25 ) ).

tff(fact_536_tl_Osimps_I1_J,axiom,
    hAPP_l84111627le_alt(tl_Arr1883752598le_alt,nil_Ar557011903le_alt) = nil_Ar557011903le_alt ).

tff(fact_537_distinct__tl,axiom,
    ! [Xs_24: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_24))
     => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(tl_Arr1883752598le_alt,Xs_24))) ) ).

tff(fact_538_listrel1__eq__len,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
     => ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_1) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys_1) ) ) ).

tff(fact_539_listrel_ONil,axiom,
    ! [R_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,nil_Ar557011903le_alt),nil_Ar557011903le_alt)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2))) ).

tff(fact_540_tl__append2,axiom,
    ! [Ys_6: list_A114658244le_alt,Xs_23: list_A114658244le_alt] :
      ( ( Xs_23 != nil_Ar557011903le_alt )
     => ( hAPP_l84111627le_alt(tl_Arr1883752598le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_23),Ys_6)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(tl_Arr1883752598le_alt,Xs_23)),Ys_6) ) ) ).

tff(fact_541_lexord__lex,axiom,
    ! [X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),hAPP_f369701637t_bool(lex_Ar686335011le_alt,R_2)))
    <=> ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
        & ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,X_2) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Y_2) ) ) ) ).

tff(fact_542_eq__equal,axiom,
    fequal928191109le_alt = equal_631514850le_alt ).

tff(fact_543_equal__eq,axiom,
    ! [X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(equal_631514850le_alt,X_2),Y_2))
    <=> ( X_2 = Y_2 ) ) ).

tff(fact_544_equal__refl,axiom,
    ! [X_23: list_A114658244le_alt] : hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(equal_631514850le_alt,X_23),X_23)) ).

tff(fact_545_listrel__Cons2,axiom,
    ! [Xs_1: list_l2028444773le_alt,Y_2: list_A114658244le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1))),hAPP_f417980453t_bool(listre770069484le_alt,R_2)))
     => ~ ! [X_1: list_A114658244le_alt,Xs_17: list_l2028444773le_alt] :
            ( ( Xs_1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_1),Xs_17) )
           => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_2)),R_2))
             => ~ hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_17),Ys_1)),hAPP_f417980453t_bool(listre770069484le_alt,R_2))) ) ) ) ).

tff(fact_546_listrel__Cons2,axiom,
    ! [Xs_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
     => ~ ! [X_1: arrow_1893660431le_alt,Xs_17: list_A114658244le_alt] :
            ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Xs_17) )
           => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_2)),R_2))
             => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_17),Ys_1)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2))) ) ) ) ).

tff(fact_547_listrel__Cons1,axiom,
    ! [Y_2: list_A114658244le_alt,Ys_1: list_l2028444773le_alt,Xs_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1)),Xs_1)),hAPP_f417980453t_bool(listre770069484le_alt,R_2)))
     => ~ ! [Y_9: list_A114658244le_alt,Ys: list_l2028444773le_alt] :
            ( ( Xs_1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_9),Ys) )
           => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_2),Y_9)),R_2))
             => ~ hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Ys_1),Ys)),hAPP_f417980453t_bool(listre770069484le_alt,R_2))) ) ) ) ).

tff(fact_548_listrel__Cons1,axiom,
    ! [Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt,Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1)),Xs_1)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
     => ~ ! [Y_9: arrow_1893660431le_alt,Ys: list_A114658244le_alt] :
            ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Ys) )
           => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_2),Y_9)),R_2))
             => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ys_1),Ys)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2))) ) ) ) ).

tff(fact_549_list__induct2,axiom,
    ! [Pa: fun_li495175091t_bool,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_1) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys_1) )
     => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,nil_Ar557011903le_alt),nil_Ar557011903le_alt))
       => ( ! [X_1: arrow_1893660431le_alt,Xs_17: list_A114658244le_alt,Y_9: arrow_1893660431le_alt,Ys: list_A114658244le_alt] :
              ( ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_17) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys) )
             => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Xs_17),Ys))
               => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Xs_17)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Ys))) ) )
         => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Xs_1),Ys_1)) ) ) ) ).

tff(fact_550_splitI2,axiom,
    ! [Ca: fun_li495175091t_bool,P_1: produc587761367le_alt] :
      ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
          ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6) )
         => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Ca,A_7),B_6)) )
     => hBOOL(hAPP_P1894408759t_bool(hAPP_f1732069219t_bool(produc631952405t_bool,Ca),P_1)) ) ).

tff(fact_551_splitI2,axiom,
    ! [Ca: fun_Ar331856045t_bool,P_1: produc472769767le_alt] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) )
         => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Ca,A_7),B_6)) )
     => hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,Ca),P_1)) ) ).

tff(fact_552_splitE,axiom,
    ! [Ca: fun_li495175091t_bool,P_1: produc587761367le_alt] :
      ( hBOOL(hAPP_P1894408759t_bool(hAPP_f1732069219t_bool(produc631952405t_bool,Ca),P_1))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Ca,X_1),Y_9)) ) ) ).

tff(fact_553_splitE,axiom,
    ! [Ca: fun_Ar331856045t_bool,P_1: produc472769767le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,Ca),P_1))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Ca,X_1),Y_9)) ) ) ).

tff(fact_554_mem__splitI2,axiom,
    ! [Z_3: nat,Ca: fun_Ar113775056t_bool,P_1: produc472769767le_alt] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_A75605626t_bool(hAPP_A98481698t_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_P1123315306t_bool(hAPP_f2044004281t_bool(produc802256322t_bool,Ca),P_1))) ) ).

tff(fact_555_mem__splitI2,axiom,
    ! [Z_3: produc587761367le_alt,Ca: fun_Ar26892405t_bool,P_1: produc472769767le_alt] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) )
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Z_3),hAPP_A876841247t_bool(hAPP_A837018253t_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Z_3),hAPP_P588680495t_bool(hAPP_f582323651t_bool(produc2013750231t_bool,Ca),P_1))) ) ).

tff(fact_556_mem__splitI2,axiom,
    ! [Z_3: arrow_1893660431le_alt,Ca: fun_Ar1044946517t_bool,P_1: produc472769767le_alt] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) )
         => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Z_3),hAPP_A2063800319t_bool(hAPP_A1975288231t_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Z_3),hAPP_P1328248815t_bool(hAPP_f919250425t_bool(produc542980935t_bool,Ca),P_1))) ) ).

tff(fact_557_mem__splitI2,axiom,
    ! [Z_3: arrow_856714788e_indi,Ca: fun_Ar1628482114i_bool,P_1: produc472769767le_alt] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Z_3),hAPP_A1492453356i_bool(hAPP_A891807578i_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Z_3),hAPP_P1859429372i_bool(hAPP_f1028383325i_bool(produc762033828i_bool,Ca),P_1))) ) ).

tff(fact_558_mem__splitI2,axiom,
    ! [Z_3: bool,Ca: fun_Ar949229051l_bool,P_1: produc472769767le_alt] :
      ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
          ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6) )
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_A463015077l_bool(hAPP_A1316408339l_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_P1103642805l_bool(hAPP_f874384847l_bool(produc327487325l_bool,Ca),P_1))) ) ).

tff(fact_559_mem__splitI2,axiom,
    ! [Z_3: produc472769767le_alt,Ca: fun_li1684108543t_bool,P_1: produc587761367le_alt] :
      ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
          ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Z_3),hAPP_l1875392034t_bool(hAPP_l1232500765t_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Z_3),hAPP_P1708597583t_bool(hAPP_f1879310829t_bool(produc47507185t_bool,Ca),P_1))) ) ).

tff(fact_560_mem__splitI2,axiom,
    ! [Z_3: fun_Ar274636406t_bool,Ca: fun_li1290371598l_bool,P_1: produc587761367le_alt] :
      ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
          ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Z_3),hAPP_l1144124209l_bool(hAPP_l362966444l_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Z_3),hAPP_P878768990l_bool(hAPP_f1371571723l_bool(produc632580864l_bool,Ca),P_1))) ) ).

tff(fact_561_mem__splitI2,axiom,
    ! [Z_3: fun_Pr2067565481t_bool,Ca: fun_li1959074549l_bool,P_1: produc587761367le_alt] :
      ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
          ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Z_3),hAPP_l1876389606l_bool(hAPP_l328381505l_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Z_3),hAPP_P171164537l_bool(hAPP_f229317091l_bool(produc999826263l_bool,Ca),P_1))) ) ).

tff(fact_562_mem__splitI2,axiom,
    ! [Z_3: fun_fu2114379172t_bool,Ca: fun_li123689532l_bool,P_1: produc587761367le_alt] :
      ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
          ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Z_3),hAPP_l592144991l_bool(hAPP_l830471642l_bool(Ca,A_7),B_6))) )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Z_3),hAPP_P1986703244l_bool(hAPP_f928402023l_bool(produc1727510830l_bool,Ca),P_1))) ) ).

tff(fact_563_mem__splitE,axiom,
    ! [Z_3: nat,Ca: fun_Ar113775056t_bool,P_1: produc472769767le_alt] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_P1123315306t_bool(hAPP_f2044004281t_bool(produc802256322t_bool,Ca),P_1)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_A75605626t_bool(hAPP_A98481698t_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_564_mem__splitE,axiom,
    ! [Z_3: produc587761367le_alt,Ca: fun_Ar26892405t_bool,P_1: produc472769767le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Z_3),hAPP_P588680495t_bool(hAPP_f582323651t_bool(produc2013750231t_bool,Ca),P_1)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Z_3),hAPP_A876841247t_bool(hAPP_A837018253t_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_565_mem__splitE,axiom,
    ! [Z_3: arrow_1893660431le_alt,Ca: fun_Ar1044946517t_bool,P_1: produc472769767le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Z_3),hAPP_P1328248815t_bool(hAPP_f919250425t_bool(produc542980935t_bool,Ca),P_1)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Z_3),hAPP_A2063800319t_bool(hAPP_A1975288231t_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_566_mem__splitE,axiom,
    ! [Z_3: arrow_856714788e_indi,Ca: fun_Ar1628482114i_bool,P_1: produc472769767le_alt] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Z_3),hAPP_P1859429372i_bool(hAPP_f1028383325i_bool(produc762033828i_bool,Ca),P_1)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Z_3),hAPP_A1492453356i_bool(hAPP_A891807578i_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_567_mem__splitE,axiom,
    ! [Z_3: bool,Ca: fun_Ar949229051l_bool,P_1: produc472769767le_alt] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_P1103642805l_bool(hAPP_f874384847l_bool(produc327487325l_bool,Ca),P_1)))
     => ~ ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt] :
            ( ( P_1 = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_A463015077l_bool(hAPP_A1316408339l_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_568_mem__splitE,axiom,
    ! [Z_3: produc472769767le_alt,Ca: fun_li1684108543t_bool,P_1: produc587761367le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Z_3),hAPP_P1708597583t_bool(hAPP_f1879310829t_bool(produc47507185t_bool,Ca),P_1)))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Z_3),hAPP_l1875392034t_bool(hAPP_l1232500765t_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_569_mem__splitE,axiom,
    ! [Z_3: fun_Ar274636406t_bool,Ca: fun_li1290371598l_bool,P_1: produc587761367le_alt] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Z_3),hAPP_P878768990l_bool(hAPP_f1371571723l_bool(produc632580864l_bool,Ca),P_1)))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Z_3),hAPP_l1144124209l_bool(hAPP_l362966444l_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_570_mem__splitE,axiom,
    ! [Z_3: fun_Pr2067565481t_bool,Ca: fun_li1959074549l_bool,P_1: produc587761367le_alt] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Z_3),hAPP_P171164537l_bool(hAPP_f229317091l_bool(produc999826263l_bool,Ca),P_1)))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Z_3),hAPP_l1876389606l_bool(hAPP_l328381505l_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_571_mem__splitE,axiom,
    ! [Z_3: fun_fu2114379172t_bool,Ca: fun_li123689532l_bool,P_1: produc587761367le_alt] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Z_3),hAPP_P1986703244l_bool(hAPP_f928402023l_bool(produc1727510830l_bool,Ca),P_1)))
     => ~ ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt] :
            ( ( P_1 = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9) )
           => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Z_3),hAPP_l592144991l_bool(hAPP_l830471642l_bool(Ca,X_1),Y_9))) ) ) ).

tff(fact_572_split__part,axiom,
    ! [Pa: bool,Q_1: fun_Ar331856045t_bool,X_1: produc472769767le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,hAPP_f2095778909t_bool(hAPP_f1336702693t_bool(cOMBB_1074233563le_alt,hAPP_f2127477477t_bool(cOMBB_388242475le_alt,fconj(Pa))),Q_1)),X_1))
    <=> ( hBOOL(Pa)
        & hBOOL(hAPP_P1178790471t_bool(hAPP_f782115833t_bool(produc73018783t_bool,Q_1),X_1)) ) ) ).

tff(fact_573_listrelp__listrel__eq,axiom,
    ! [R_2: fun_Pr486337689t_bool,X_1: list_l2028444773le_alt,Xa: list_l2028444773le_alt] :
      ( hBOOL(hAPP_l527728301t_bool(hAPP_l246742955t_bool(listre963584058le_alt(hAPP_f1232688951t_bool(hAPP_f1613523967t_bool(cOMBC_1701707246t_bool,hAPP_f406989951t_bool(hAPP_f2107183495t_bool(cOMBB_2102331378le_alt,cOMBC_493955701l_bool),hAPP_f561566485l_bool(hAPP_f1983518615l_bool(cOMBB_1429729016le_alt,hAPP_f1589431871l_bool(cOMBB_835145300le_alt,member1401409220le_alt)),produc1742925389le_alt))),R_2)),X_1),Xa))
    <=> hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,X_1),Xa)),hAPP_f417980453t_bool(listre770069484le_alt,R_2))) ) ).

tff(fact_574_listrelp__listrel__eq,axiom,
    ! [R_2: fun_Pr2067565481t_bool,X_1: list_A114658244le_alt,Xa: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(listre483979801le_alt(hAPP_f449303873t_bool(hAPP_f1081591777t_bool(cOMBC_557453916t_bool,hAPP_f105674721t_bool(hAPP_f322072549t_bool(cOMBB_652885079le_alt,cOMBC_395465908l_bool),hAPP_f184584489l_bool(hAPP_f759033445l_bool(cOMBB_1575576719le_alt,hAPP_f1344055909l_bool(cOMBB_1660064607le_alt,member1333168212le_alt)),produc1590937303le_alt))),R_2)),X_1),Xa))
    <=> hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Xa)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2))) ) ).

tff(fact_575_rotate1__hd__tl,axiom,
    ! [Xs_22: list_A114658244le_alt] :
      ( ( Xs_22 != nil_Ar557011903le_alt )
     => ( hAPP_l84111627le_alt(rotate1753650700le_alt,Xs_22) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(tl_Arr1883752598le_alt,Xs_22)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,hd_Arr1236501138le_alt(Xs_22)),nil_Ar557011903le_alt)) ) ) ).

tff(fact_576_listrel_Osimps,axiom,
    ! [A1: list_l2028444773le_alt,A2: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,A1),A2)),hAPP_f417980453t_bool(listre770069484le_alt,R_2)))
    <=> ( ( ( A1 = nil_li2054189844le_alt )
          & ( A2 = nil_li2054189844le_alt ) )
        | ? [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt,Xs_17: list_l2028444773le_alt,Ys: list_l2028444773le_alt] :
            ( ( A1 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_1),Xs_17) )
            & ( A2 = hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_9),Ys) )
            & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9)),R_2))
            & hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_17),Ys)),hAPP_f417980453t_bool(listre770069484le_alt,R_2))) ) ) ) ).

tff(fact_577_listrel_Osimps,axiom,
    ! [A1: list_A114658244le_alt,A2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A1),A2)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
    <=> ( ( ( A1 = nil_Ar557011903le_alt )
          & ( A2 = nil_Ar557011903le_alt ) )
        | ? [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt,Xs_17: list_A114658244le_alt,Ys: list_A114658244le_alt] :
            ( ( A1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Xs_17) )
            & ( A2 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Ys) )
            & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9)),R_2))
            & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_17),Ys)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2))) ) ) ) ).

tff(fact_578_lexn__length,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool,N_2: nat] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),lexn_A1588662879le_alt(R_2,N_2)))
     => ( ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_1) = N_2 )
        & ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Ys_1) = N_2 ) ) ) ).

tff(fact_579_Ex__list__of__length,axiom,
    ! [N_13: nat] :
    ? [Xs_17: list_A114658244le_alt] : ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_17) = N_13 ) ).

tff(fact_580_replicate__append__same,axiom,
    ! [I_11: nat,X_22: arrow_1893660431le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(I_11),X_22)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_22),nil_Ar557011903le_alt)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_22),hAPP_A1382181054le_alt(replic782356601le_alt(I_11),X_22)) ) ).

tff(fact_581_length__replicate,axiom,
    ! [N_12: nat,X_21: arrow_1893660431le_alt] : ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(N_12),X_21)) = N_12 ) ).

tff(fact_582_append__replicate__commute,axiom,
    ! [N_11: nat,X_20: arrow_1893660431le_alt,K_3: nat] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(N_11),X_20)),hAPP_A1382181054le_alt(replic782356601le_alt(K_3),X_20)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(K_3),X_20)),hAPP_A1382181054le_alt(replic782356601le_alt(N_11),X_20)) ) ).

tff(fact_583_hd_Osimps,axiom,
    ! [X_19: arrow_1893660431le_alt,Xs_21: list_A114658244le_alt] : ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_19),Xs_21)) = X_19 ) ).

tff(fact_584_replicate__app__Cons__same,axiom,
    ! [N_10: nat,X_18: arrow_1893660431le_alt,Xs_20: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(N_10),X_18)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_18),Xs_20)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_18),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(N_10),X_18)),Xs_20)) ) ).

tff(fact_585_listrelp_OCons,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Ar331856045t_bool,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(R_2,X_2),Y_2))
     => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(listre483979801le_alt(R_2),Xs_1),Ys_1))
       => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(listre483979801le_alt(R_2),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))) ) ) ).

tff(fact_586_listrelp_ONil,axiom,
    ! [R_2: fun_Ar331856045t_bool] : hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(listre483979801le_alt(R_2),nil_Ar557011903le_alt),nil_Ar557011903le_alt)) ).

tff(fact_587_hd__append,axiom,
    ! [Ys_5: list_A114658244le_alt,Xs_19: list_A114658244le_alt] :
      ( ( ( Xs_19 = nil_Ar557011903le_alt )
       => ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_19),Ys_5)) = hd_Arr1236501138le_alt(Ys_5) ) )
      & ( ( Xs_19 != nil_Ar557011903le_alt )
       => ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_19),Ys_5)) = hd_Arr1236501138le_alt(Xs_19) ) ) ) ).

tff(fact_588_hd__append2,axiom,
    ! [Ys_4: list_A114658244le_alt,Xs_18: list_A114658244le_alt] :
      ( ( Xs_18 != nil_Ar557011903le_alt )
     => ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_18),Ys_4)) = hd_Arr1236501138le_alt(Xs_18) ) ) ).

tff(fact_589_hd__dropWhile,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1) != nil_Ar557011903le_alt )
     => ~ hBOOL(hAPP_A1748732503t_bool(Pa,hd_Arr1236501138le_alt(hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1)))) ) ).

tff(fact_590_listrelp_Osimps,axiom,
    ! [R_2: fun_Ar331856045t_bool,A1: list_A114658244le_alt,A2: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(listre483979801le_alt(R_2),A1),A2))
    <=> ( ( ( A1 = nil_Ar557011903le_alt )
          & ( A2 = nil_Ar557011903le_alt ) )
        | ? [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt,Xs_17: list_A114658244le_alt,Ys: list_A114658244le_alt] :
            ( ( A1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Xs_17) )
            & ( A2 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_9),Ys) )
            & hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(R_2,X_1),Y_9))
            & hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(listre483979801le_alt(R_2),Xs_17),Ys)) ) ) ) ).

tff(fact_591_last__rev,axiom,
    ! [Xs_16: list_A114658244le_alt] :
      ( ( Xs_16 != nil_Ar557011903le_alt )
     => ( last_A488133080le_alt(hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_16)) = hd_Arr1236501138le_alt(Xs_16) ) ) ).

tff(fact_592_hd__rev,axiom,
    ! [Xs_15: list_A114658244le_alt] :
      ( ( Xs_15 != nil_Ar557011903le_alt )
     => ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_15)) = last_A488133080le_alt(Xs_15) ) ) ).

tff(fact_593_dropWhile__eq__drop,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1) = hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,hAPP_l1084348419lt_nat(size_s2005684270le_alt,hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1))),Xs_1) ) ).

tff(fact_594_list__update__length,axiom,
    ! [Xs_14: list_A114658244le_alt,X_17: arrow_1893660431le_alt,Ys_3: list_A114658244le_alt,Y_12: arrow_1893660431le_alt] : ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_14),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_17),Ys_3))),hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_14)),Y_12) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_14),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_12),Ys_3)) ) ).

tff(fact_595_map__pair__def,axiom,
    ! [F: fun_li90789869le_alt,G: fun_li90789869le_alt] : ( produc1411910245le_alt(F,G) = hAPP_f1221439459le_alt(produc2052829583le_alt,hAPP_f1274386949le_alt(hAPP_f905689843le_alt(cOMBC_1284478484le_alt,hAPP_f1148079597le_alt(hAPP_f1250095511le_alt(cOMBB_1247716816le_alt,cOMBB_250395785le_alt),hAPP_f1274386949le_alt(hAPP_f1142066787le_alt(cOMBB_1071360260le_alt,produc1742925389le_alt),F))),G)) ) ).

tff(fact_596_rtrancl__listrel1__if__listrel,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1191473383le_alt,R_2)))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))) ) ).

tff(fact_597_listrel__rtrancl__refl,axiom,
    ! [Xs_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Xs_1)),hAPP_f369701637t_bool(listre1191473383le_alt,transi1687363644le_alt(R_2)))) ).

tff(fact_598_list__update__swap,axiom,
    ! [Xs_13: list_A114658244le_alt,X_16: arrow_1893660431le_alt,X_15: arrow_1893660431le_alt,I_10: nat,I_9: nat] :
      ( ( I_10 != I_9 )
     => ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(Xs_13),I_10),X_16)),I_9),X_15) = hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(Xs_13),I_9),X_15)),I_10),X_16) ) ) ).

tff(fact_599_list__update__overwrite,axiom,
    ! [Xs_12: list_A114658244le_alt,I_8: nat,X_14: arrow_1893660431le_alt,Y_11: arrow_1893660431le_alt] : ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(Xs_12),I_8),X_14)),I_8),Y_11) = hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(Xs_12),I_8),Y_11) ) ).

tff(fact_600_rev__is__rev__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) = hAPP_l84111627le_alt(rev_Ar377224735le_alt,Ys_1) )
    <=> ( Xs_1 = Ys_1 ) ) ).

tff(fact_601_rev__swap,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) = Ys_1 )
    <=> ( Xs_1 = hAPP_l84111627le_alt(rev_Ar377224735le_alt,Ys_1) ) ) ).

tff(fact_602_rev__rev__ident,axiom,
    ! [Xs_11: list_A114658244le_alt] : ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_11)) = Xs_11 ) ).

tff(fact_603_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [R_2: fun_Pr2067565481t_bool] : ( hAPP_f369701637t_bool(listre1191473383le_alt,transi1687363644le_alt(R_2)) = transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2)) ) ).

tff(fact_604_drop__Nil,axiom,
    ! [N_9: nat] : ( hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_9),nil_Ar557011903le_alt) = nil_Ar557011903le_alt ) ).

tff(fact_605_rev_Osimps_I1_J,axiom,
    hAPP_l84111627le_alt(rev_Ar377224735le_alt,nil_Ar557011903le_alt) = nil_Ar557011903le_alt ).

tff(fact_606_Nil__is__rev__conv,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( nil_Ar557011903le_alt = hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) )
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_607_rev__is__Nil__conv,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) = nil_Ar557011903le_alt )
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_608_length__rev,axiom,
    ! [Xs_10: list_A114658244le_alt] : ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_10)) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_10) ) ).

tff(fact_609_rev__append,axiom,
    ! [Xs_9: list_A114658244le_alt,Ys_2: list_A114658244le_alt] : ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_9),Ys_2)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(rev_Ar377224735le_alt,Ys_2)),hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_9)) ) ).

tff(fact_610_distinct__drop,axiom,
    ! [I_7: nat,Xs_8: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_8))
     => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,I_7),Xs_8))) ) ).

tff(fact_611_list__update__nonempty,axiom,
    ! [Xs_1: list_A114658244le_alt,K: nat,X_2: arrow_1893660431le_alt] :
      ( ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(Xs_1),K),X_2) = nil_Ar557011903le_alt )
    <=> ( Xs_1 = nil_Ar557011903le_alt ) ) ).

tff(fact_612_list__update_Osimps_I1_J,axiom,
    ! [I_6: nat,V_1: arrow_1893660431le_alt] : ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(nil_Ar557011903le_alt),I_6),V_1) = nil_Ar557011903le_alt ) ).

tff(fact_613_list__update__code_I1_J,axiom,
    ! [I_5: nat,Y_10: arrow_1893660431le_alt] : ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(nil_Ar557011903le_alt),I_5),Y_10) = nil_Ar557011903le_alt ) ).

tff(fact_614_length__list__update,axiom,
    ! [Xs_7: list_A114658244le_alt,I_4: nat,X_13: arrow_1893660431le_alt] : ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(Xs_7),I_4),X_13)) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Xs_7) ) ).

tff(fact_615_distinct__rev,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1)))
    <=> hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1)) ) ).

tff(fact_616_rev__replicate,axiom,
    ! [N_8: nat,X_12: arrow_1893660431le_alt] : ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,hAPP_A1382181054le_alt(replic782356601le_alt(N_8),X_12)) = hAPP_A1382181054le_alt(replic782356601le_alt(N_8),X_12) ) ).

tff(fact_617_drop__butlast,axiom,
    ! [N_7: nat,Xs_6: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_7),hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_6)) = hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_7),Xs_6)) ) ).

tff(fact_618_butlast__drop,axiom,
    ! [N_6: nat,Xs_5: list_A114658244le_alt] : ( hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_6),Xs_5)) = hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_6),hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_5)) ) ).

tff(fact_619_drop__tl,axiom,
    ! [N_5: nat,Xs_4: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_5),hAPP_l84111627le_alt(tl_Arr1883752598le_alt,Xs_4)) = hAPP_l84111627le_alt(tl_Arr1883752598le_alt,hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_5),Xs_4)) ) ).

tff(fact_620_tl__drop,axiom,
    ! [N_4: nat,Xs_3: list_A114658244le_alt] : ( hAPP_l84111627le_alt(tl_Arr1883752598le_alt,hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_4),Xs_3)) = hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_4),hAPP_l84111627le_alt(tl_Arr1883752598le_alt,Xs_3)) ) ).

tff(fact_621_rtrancl__listrel1__ConsI2,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),transi1687363644le_alt(R_2)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2))))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1))),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))) ) ) ).

tff(fact_622_rtrancl__listrel1__ConsI2,axiom,
    ! [Xs_1: list_l2028444773le_alt,Ys_1: list_l2028444773le_alt,X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),transi1124010071le_alt(R_2)))
     => ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),transi1249888786le_alt(hAPP_f417980453t_bool(listre767458683le_alt,R_2))))
       => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,X_2),Xs_1)),hAPP_l1913469717le_alt(hAPP_l1201992822le_alt(cons_l782000996le_alt,Y_2),Ys_1))),transi1249888786le_alt(hAPP_f417980453t_bool(listre767458683le_alt,R_2)))) ) ) ).

tff(fact_623_rev__singleton__conv,axiom,
    ! [Xs_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt] :
      ( ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt) )
    <=> ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt) ) ) ).

tff(fact_624_singleton__rev__conv,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt) = hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) )
    <=> ( Xs_1 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),nil_Ar557011903le_alt) ) ) ).

tff(fact_625_listrel__rtrancl__trans,axiom,
    ! [Zs_1: list_A114658244le_alt,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1191473383le_alt,transi1687363644le_alt(R_2))))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ys_1),Zs_1)),hAPP_f369701637t_bool(listre1191473383le_alt,transi1687363644le_alt(R_2))))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Zs_1)),hAPP_f369701637t_bool(listre1191473383le_alt,transi1687363644le_alt(R_2)))) ) ) ).

tff(fact_626_rtrancl__listrel1__ConsI1,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2))))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Ys_1))),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))) ) ).

tff(fact_627_rtrancl__listrel1__eq__len,axiom,
    ! [X_2: list_A114658244le_alt,Y_2: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_2)),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2))))
     => ( hAPP_l1084348419lt_nat(size_s2005684270le_alt,X_2) = hAPP_l1084348419lt_nat(size_s2005684270le_alt,Y_2) ) ) ).

tff(fact_628_rev_Osimps_I2_J,axiom,
    ! [X_11: arrow_1893660431le_alt,Xs_2: list_A114658244le_alt] : ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_11),Xs_2)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_2)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_11),nil_Ar557011903le_alt)) ) ).

tff(fact_629_rev__eq__Cons__iff,axiom,
    ! [Xs_1: list_A114658244le_alt,Y_2: arrow_1893660431le_alt,Ys_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),Ys_1) )
    <=> ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(rev_Ar377224735le_alt,Ys_1)),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,Y_2),nil_Ar557011903le_alt)) ) ) ).

tff(fact_630_listrel__reflcl__if__listrel1,axiom,
    ! [Xs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(listre1191473383le_alt,transi1687363644le_alt(R_2)))) ) ).

tff(fact_631_rtrancl_Ortrancl__refl,axiom,
    ! [Aa: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] : hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Aa)),transi1124010071le_alt(R_2))) ).

tff(fact_632_rtrancl_Ortrancl__refl,axiom,
    ! [Aa: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Aa)),transi1687363644le_alt(R_2))) ).

tff(fact_633_r__into__rtrancl,axiom,
    ! [P_1: produc587761367le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,P_1),R_2))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,P_1),transi1124010071le_alt(R_2))) ) ).

tff(fact_634_r__into__rtrancl,axiom,
    ! [P_1: produc472769767le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,P_1),R_2))
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,P_1),transi1687363644le_alt(R_2))) ) ).

tff(fact_635_converse__rtrancl__into__rtrancl,axiom,
    ! [Ca: list_A114658244le_alt,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),R_2))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ba),Ca)),transi1124010071le_alt(R_2)))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ca)),transi1124010071le_alt(R_2))) ) ) ).

tff(fact_636_converse__rtrancl__into__rtrancl,axiom,
    ! [Ca: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),R_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Ca)),transi1687363644le_alt(R_2)))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ca)),transi1687363644le_alt(R_2))) ) ) ).

tff(fact_637_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [Ca: list_A114658244le_alt,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),transi1124010071le_alt(R_2)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ba),Ca)),R_2))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ca)),transi1124010071le_alt(R_2))) ) ) ).

tff(fact_638_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [Ca: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),transi1687363644le_alt(R_2)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Ca)),R_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ca)),transi1687363644le_alt(R_2))) ) ) ).

tff(fact_639_rtrancl__trans,axiom,
    ! [Ca: list_A114658244le_alt,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),transi1124010071le_alt(R_2)))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ba),Ca)),transi1124010071le_alt(R_2)))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ca)),transi1124010071le_alt(R_2))) ) ) ).

tff(fact_640_rtrancl__trans,axiom,
    ! [Ca: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),transi1687363644le_alt(R_2)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Ca)),transi1687363644le_alt(R_2)))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ca)),transi1687363644le_alt(R_2))) ) ) ).

tff(fact_641_takeWhile__neq__rev,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
       => ( hAPP_l84111627le_alt(takeWh967109304le_alt(hAPP_f1592536333t_bool(hAPP_f2127477477t_bool(cOMBB_388242475le_alt,fNot),hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(cOMBC_1826973210t_bool,fequal1590852494le_alt),X_2))),hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1)) = hAPP_l84111627le_alt(rev_Ar377224735le_alt,hAPP_l84111627le_alt(tl_Arr1883752598le_alt,hAPP_l84111627le_alt(dropWh587599712le_alt(hAPP_f1592536333t_bool(hAPP_f2127477477t_bool(cOMBB_388242475le_alt,fNot),hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(cOMBC_1826973210t_bool,fequal1590852494le_alt),X_2))),Xs_1))) ) ) ) ).

tff(fact_642_takeWhile__neq__rev,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
       => ( hAPP_l248265089st_nat(takeWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),hAPP_l248265089st_nat(rev_nat,Xs_1)) = hAPP_l248265089st_nat(rev_nat,hAPP_l248265089st_nat(tl_nat,hAPP_l248265089st_nat(dropWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),Xs_1))) ) ) ) ).

tff(fact_643_takeWhile__neq__rev,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_l255772864t_bool(distin1934286196le_alt,Xs_1))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
       => ( hAPP_l922056661le_alt(takeWh797115118le_alt(hAPP_f2146417685t_bool(hAPP_f202057843t_bool(cOMBB_1985622715le_alt,fNot),hAPP_P1907587391t_bool(hAPP_f870273001t_bool(cOMBC_2103205814t_bool,fequal1054218392le_alt),X_2))),hAPP_l922056661le_alt(rev_Pr844913607le_alt,Xs_1)) = hAPP_l922056661le_alt(rev_Pr844913607le_alt,hAPP_l922056661le_alt(tl_Pro673569168le_alt,hAPP_l922056661le_alt(dropWh1985299526le_alt(hAPP_f2146417685t_bool(hAPP_f202057843t_bool(cOMBB_1985622715le_alt,fNot),hAPP_P1907587391t_bool(hAPP_f870273001t_bool(cOMBC_2103205814t_bool,fequal1054218392le_alt),X_2))),Xs_1))) ) ) ) ).

tff(fact_644_takeWhile__neq__rev,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_l311606797i_bool(distin1343912001e_indi,Xs_1))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
       => ( hAPP_l713773333e_indi(takeWh259024059e_indi(hAPP_f1612707285i_bool(hAPP_f1347397683i_bool(cOMBB_1127256072e_indi,fNot),hAPP_A575544447i_bool(hAPP_f512805993i_bool(cOMBC_1266306896i_bool,fequal1182599525e_indi),X_2))),hAPP_l713773333e_indi(rev_Ar2076519188e_indi,Xs_1)) = hAPP_l713773333e_indi(rev_Ar2076519188e_indi,hAPP_l713773333e_indi(tl_Arr1600323165e_indi,hAPP_l713773333e_indi(dropWh587229715e_indi(hAPP_f1612707285i_bool(hAPP_f1347397683i_bool(cOMBB_1127256072e_indi,fNot),hAPP_A575544447i_bool(hAPP_f512805993i_bool(cOMBC_1266306896i_bool,fequal1182599525e_indi),X_2))),Xs_1))) ) ) ) ).

tff(fact_645_takeWhile__neq__rev,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_list_bool_bool(distinct_bool,Xs_1))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
       => ( hAPP_l1189022293t_bool(takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),hAPP_l1189022293t_bool(rev_bool,Xs_1)) = hAPP_l1189022293t_bool(rev_bool,hAPP_l1189022293t_bool(tl_bool,hAPP_l1189022293t_bool(dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_646_takeWhile__neq__rev,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_l1502732685l_bool(distin1644384705t_bool,Xs_1))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
       => ( hAPP_l1936976149t_bool(takeWh1969918523t_bool(hAPP_f1181604821l_bool(hAPP_f1662395443l_bool(cOMBB_1112311688t_bool,fNot),hAPP_f1105736319l_bool(hAPP_f1764760681l_bool(cOMBC_57903184l_bool,fequal1249241829t_bool),X_2))),hAPP_l1936976149t_bool(rev_fu1281784468t_bool,Xs_1)) = hAPP_l1936976149t_bool(rev_fu1281784468t_bool,hAPP_l1936976149t_bool(tl_fun66473949t_bool,hAPP_l1936976149t_bool(dropWh1823459219t_bool(hAPP_f1181604821l_bool(hAPP_f1662395443l_bool(cOMBB_1112311688t_bool,fNot),hAPP_f1105736319l_bool(hAPP_f1764760681l_bool(cOMBC_57903184l_bool,fequal1249241829t_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_647_takeWhile__neq__rev,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_l1252368702l_bool(distin116221260t_bool,Xs_1))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
       => ( hAPP_l1229506623t_bool(takeWh2085154898t_bool(hAPP_f1060563265l_bool(hAPP_f1594093337l_bool(cOMBB_882486469t_bool,fNot),hAPP_f930900275l_bool(hAPP_f599780549l_bool(cOMBC_1554707866l_bool,fequal1830749992t_bool),X_2))),hAPP_l1229506623t_bool(rev_fu1613832889t_bool,Xs_1)) = hAPP_l1229506623t_bool(rev_fu1613832889t_bool,hAPP_l1229506623t_bool(tl_fun496344112t_bool,hAPP_l1229506623t_bool(dropWh1706032378t_bool(hAPP_f1060563265l_bool(hAPP_f1594093337l_bool(cOMBB_882486469t_bool,fNot),hAPP_f930900275l_bool(hAPP_f599780549l_bool(cOMBC_1554707866l_bool,fequal1830749992t_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_648_takeWhile__neq__rev,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_l446901855l_bool(distin194731411t_bool,Xs_1))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
       => ( hAPP_l179891349t_bool(takeWh1481438221t_bool(hAPP_f819682389l_bool(hAPP_f1356804275l_bool(cOMBB_1044350042t_bool,fNot),hAPP_f2087119359l_bool(hAPP_f410199913l_bool(cOMBC_353845492l_bool,fequal957608631t_bool),X_2))),hAPP_l179891349t_bool(rev_fu2129709926t_bool,Xs_1)) = hAPP_l179891349t_bool(rev_fu2129709926t_bool,hAPP_l179891349t_bool(tl_fun210444207t_bool,hAPP_l179891349t_bool(dropWh1724617061t_bool(hAPP_f819682389l_bool(hAPP_f1356804275l_bool(cOMBB_1044350042t_bool,fNot),hAPP_f2087119359l_bool(hAPP_f410199913l_bool(cOMBC_353845492l_bool,fequal957608631t_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_649_takeWhile__neq__rev,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_l423847376t_bool(distin748429060le_alt,Xs_1))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
       => ( hAPP_l1424955733le_alt(takeWh1421241214le_alt(hAPP_f1356305429t_bool(hAPP_f1645126899t_bool(cOMBB_325568203le_alt,fNot),hAPP_P393387327t_bool(hAPP_f1270778601t_bool(cOMBC_1805080534t_bool,fequal346320936le_alt),X_2))),hAPP_l1424955733le_alt(rev_Pr187933143le_alt,Xs_1)) = hAPP_l1424955733le_alt(rev_Pr187933143le_alt,hAPP_l1424955733le_alt(tl_Pro2051728672le_alt,hAPP_l1424955733le_alt(dropWh1799418070le_alt(hAPP_f1356305429t_bool(hAPP_f1645126899t_bool(cOMBB_325568203le_alt,fNot),hAPP_P393387327t_bool(hAPP_f1270778601t_bool(cOMBC_1805080534t_bool,fequal346320936le_alt),X_2))),Xs_1))) ) ) ) ).

tff(fact_650_dropWhile__neq__rev,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
       => ( hAPP_l84111627le_alt(dropWh587599712le_alt(hAPP_f1592536333t_bool(hAPP_f2127477477t_bool(cOMBB_388242475le_alt,fNot),hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(cOMBC_1826973210t_bool,fequal1590852494le_alt),X_2))),hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1)) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),hAPP_l84111627le_alt(rev_Ar377224735le_alt,hAPP_l84111627le_alt(takeWh967109304le_alt(hAPP_f1592536333t_bool(hAPP_f2127477477t_bool(cOMBB_388242475le_alt,fNot),hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(cOMBC_1826973210t_bool,fequal1590852494le_alt),X_2))),Xs_1))) ) ) ) ).

tff(fact_651_dropWhile__neq__rev,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
       => ( hAPP_l248265089st_nat(dropWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),hAPP_l248265089st_nat(rev_nat,Xs_1)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),hAPP_l248265089st_nat(rev_nat,hAPP_l248265089st_nat(takeWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),Xs_1))) ) ) ) ).

tff(fact_652_dropWhile__neq__rev,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_l255772864t_bool(distin1934286196le_alt,Xs_1))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
       => ( hAPP_l922056661le_alt(dropWh1985299526le_alt(hAPP_f2146417685t_bool(hAPP_f202057843t_bool(cOMBB_1985622715le_alt,fNot),hAPP_P1907587391t_bool(hAPP_f870273001t_bool(cOMBC_2103205814t_bool,fequal1054218392le_alt),X_2))),hAPP_l922056661le_alt(rev_Pr844913607le_alt,Xs_1)) = hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),hAPP_l922056661le_alt(rev_Pr844913607le_alt,hAPP_l922056661le_alt(takeWh797115118le_alt(hAPP_f2146417685t_bool(hAPP_f202057843t_bool(cOMBB_1985622715le_alt,fNot),hAPP_P1907587391t_bool(hAPP_f870273001t_bool(cOMBC_2103205814t_bool,fequal1054218392le_alt),X_2))),Xs_1))) ) ) ) ).

tff(fact_653_dropWhile__neq__rev,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_l311606797i_bool(distin1343912001e_indi,Xs_1))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
       => ( hAPP_l713773333e_indi(dropWh587229715e_indi(hAPP_f1612707285i_bool(hAPP_f1347397683i_bool(cOMBB_1127256072e_indi,fNot),hAPP_A575544447i_bool(hAPP_f512805993i_bool(cOMBC_1266306896i_bool,fequal1182599525e_indi),X_2))),hAPP_l713773333e_indi(rev_Ar2076519188e_indi,Xs_1)) = hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),hAPP_l713773333e_indi(rev_Ar2076519188e_indi,hAPP_l713773333e_indi(takeWh259024059e_indi(hAPP_f1612707285i_bool(hAPP_f1347397683i_bool(cOMBB_1127256072e_indi,fNot),hAPP_A575544447i_bool(hAPP_f512805993i_bool(cOMBC_1266306896i_bool,fequal1182599525e_indi),X_2))),Xs_1))) ) ) ) ).

tff(fact_654_dropWhile__neq__rev,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_list_bool_bool(distinct_bool,Xs_1))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
       => ( hAPP_l1189022293t_bool(dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),hAPP_l1189022293t_bool(rev_bool,Xs_1)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),hAPP_l1189022293t_bool(rev_bool,hAPP_l1189022293t_bool(takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_655_dropWhile__neq__rev,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_l1502732685l_bool(distin1644384705t_bool,Xs_1))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
       => ( hAPP_l1936976149t_bool(dropWh1823459219t_bool(hAPP_f1181604821l_bool(hAPP_f1662395443l_bool(cOMBB_1112311688t_bool,fNot),hAPP_f1105736319l_bool(hAPP_f1764760681l_bool(cOMBC_57903184l_bool,fequal1249241829t_bool),X_2))),hAPP_l1936976149t_bool(rev_fu1281784468t_bool,Xs_1)) = hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),hAPP_l1936976149t_bool(rev_fu1281784468t_bool,hAPP_l1936976149t_bool(takeWh1969918523t_bool(hAPP_f1181604821l_bool(hAPP_f1662395443l_bool(cOMBB_1112311688t_bool,fNot),hAPP_f1105736319l_bool(hAPP_f1764760681l_bool(cOMBC_57903184l_bool,fequal1249241829t_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_656_dropWhile__neq__rev,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_l1252368702l_bool(distin116221260t_bool,Xs_1))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
       => ( hAPP_l1229506623t_bool(dropWh1706032378t_bool(hAPP_f1060563265l_bool(hAPP_f1594093337l_bool(cOMBB_882486469t_bool,fNot),hAPP_f930900275l_bool(hAPP_f599780549l_bool(cOMBC_1554707866l_bool,fequal1830749992t_bool),X_2))),hAPP_l1229506623t_bool(rev_fu1613832889t_bool,Xs_1)) = hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),hAPP_l1229506623t_bool(rev_fu1613832889t_bool,hAPP_l1229506623t_bool(takeWh2085154898t_bool(hAPP_f1060563265l_bool(hAPP_f1594093337l_bool(cOMBB_882486469t_bool,fNot),hAPP_f930900275l_bool(hAPP_f599780549l_bool(cOMBC_1554707866l_bool,fequal1830749992t_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_657_dropWhile__neq__rev,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_l446901855l_bool(distin194731411t_bool,Xs_1))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
       => ( hAPP_l179891349t_bool(dropWh1724617061t_bool(hAPP_f819682389l_bool(hAPP_f1356804275l_bool(cOMBB_1044350042t_bool,fNot),hAPP_f2087119359l_bool(hAPP_f410199913l_bool(cOMBC_353845492l_bool,fequal957608631t_bool),X_2))),hAPP_l179891349t_bool(rev_fu2129709926t_bool,Xs_1)) = hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),hAPP_l179891349t_bool(rev_fu2129709926t_bool,hAPP_l179891349t_bool(takeWh1481438221t_bool(hAPP_f819682389l_bool(hAPP_f1356804275l_bool(cOMBB_1044350042t_bool,fNot),hAPP_f2087119359l_bool(hAPP_f410199913l_bool(cOMBC_353845492l_bool,fequal957608631t_bool),X_2))),Xs_1))) ) ) ) ).

tff(fact_658_dropWhile__neq__rev,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_l423847376t_bool(distin748429060le_alt,Xs_1))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
       => ( hAPP_l1424955733le_alt(dropWh1799418070le_alt(hAPP_f1356305429t_bool(hAPP_f1645126899t_bool(cOMBB_325568203le_alt,fNot),hAPP_P393387327t_bool(hAPP_f1270778601t_bool(cOMBC_1805080534t_bool,fequal346320936le_alt),X_2))),hAPP_l1424955733le_alt(rev_Pr187933143le_alt,Xs_1)) = hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),hAPP_l1424955733le_alt(rev_Pr187933143le_alt,hAPP_l1424955733le_alt(takeWh1421241214le_alt(hAPP_f1356305429t_bool(hAPP_f1645126899t_bool(cOMBB_325568203le_alt,fNot),hAPP_P393387327t_bool(hAPP_f1270778601t_bool(cOMBC_1805080534t_bool,fequal346320936le_alt),X_2))),Xs_1))) ) ) ) ).

tff(fact_659_set__ConsD,axiom,
    ! [Y_2: nat,X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),set_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),set_nat(Xs_1))) ) ) ).

tff(fact_660_set__ConsD,axiom,
    ! [Y_2: arrow_1893660431le_alt,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Y_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Y_2),set_Ar1995755744le_alt(Xs_1))) ) ) ).

tff(fact_661_set__ConsD,axiom,
    ! [Y_2: produc587761367le_alt,X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Y_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Y_2),set_Pr1785012934le_alt(Xs_1))) ) ) ).

tff(fact_662_set__ConsD,axiom,
    ! [Y_2: arrow_856714788e_indi,X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Y_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Y_2),set_Ar205654163e_indi(Xs_1))) ) ) ).

tff(fact_663_set__ConsD,axiom,
    ! [Y_2: bool,X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1))))
     => ( ( hBOOL(Y_2)
        <=> hBOOL(X_2) )
        | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(Xs_1))) ) ) ).

tff(fact_664_set__ConsD,axiom,
    ! [Y_2: fun_fu2114379172t_bool,X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Y_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Y_2),set_fu2135320083t_bool(Xs_1))) ) ) ).

tff(fact_665_set__ConsD,axiom,
    ! [Y_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Y_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Y_2),set_fu1957445242t_bool(Xs_1))) ) ) ).

tff(fact_666_set__ConsD,axiom,
    ! [Y_2: fun_Ar274636406t_bool,X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Y_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Y_2),set_fu2037886949t_bool(Xs_1))) ) ) ).

tff(fact_667_set__ConsD,axiom,
    ! [Y_2: produc472769767le_alt,X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Y_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Xs_1))))
     => ( ( Y_2 = X_2 )
        | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Y_2),set_Pr496668502le_alt(Xs_1))) ) ) ).

tff(fact_668_set__rev,axiom,
    ! [Xs_1: list_A114658244le_alt] : ( set_Ar1995755744le_alt(hAPP_l84111627le_alt(rev_Ar377224735le_alt,Xs_1)) = set_Ar1995755744le_alt(Xs_1) ) ).

tff(fact_669_in__set__dropD,axiom,
    ! [X_2: nat,N_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_2),Xs_1))))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) ) ).

tff(fact_670_in__set__dropD,axiom,
    ! [X_2: arrow_1893660431le_alt,N_2: nat,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_2),Xs_1))))
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1))) ) ).

tff(fact_671_in__set__dropD,axiom,
    ! [X_2: produc587761367le_alt,N_2: nat,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(hAPP_n648772104le_alt(drop_P663726311le_alt,N_2),Xs_1))))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1))) ) ).

tff(fact_672_in__set__dropD,axiom,
    ! [X_2: arrow_856714788e_indi,N_2: nat,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(hAPP_n914286664e_indi(drop_A1023486004e_indi,N_2),Xs_1))))
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1))) ) ).

tff(fact_673_in__set__dropD,axiom,
    ! [X_2: bool,N_2: nat,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) ) ).

tff(fact_674_in__set__dropD,axiom,
    ! [X_2: fun_fu2114379172t_bool,N_2: nat,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(hAPP_n679397960t_bool(drop_f1976219572t_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1))) ) ).

tff(fact_675_in__set__dropD,axiom,
    ! [X_2: fun_Pr2067565481t_bool,N_2: nat,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(hAPP_n435915628t_bool(drop_f1214627225t_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1))) ) ).

tff(fact_676_in__set__dropD,axiom,
    ! [X_2: fun_Ar274636406t_bool,N_2: nat,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(hAPP_n1109524424t_bool(drop_f1253107846t_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1))) ) ).

tff(fact_677_in__set__dropD,axiom,
    ! [X_2: produc472769767le_alt,N_2: nat,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(hAPP_n1575317256le_alt(drop_P2052955895le_alt,N_2),Xs_1))))
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1))) ) ).

tff(fact_678_takeWhile__eq__all__conv,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1) = Xs_1 )
    <=> ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
         => hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) ) ) ).

tff(fact_679_set__takeWhileD,axiom,
    ! [X_2: nat,Pa: fun_nat_bool,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(takeWhile_nat(Pa),Xs_1))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
        & hBOOL(hAPP_nat_bool(Pa,X_2)) ) ) ).

tff(fact_680_set__takeWhileD,axiom,
    ! [X_2: arrow_1893660431le_alt,Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1))))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
        & hBOOL(hAPP_A1748732503t_bool(Pa,X_2)) ) ) ).

tff(fact_681_set__takeWhileD,axiom,
    ! [X_2: produc587761367le_alt,Pa: fun_Pr486337689t_bool,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(takeWh797115118le_alt(Pa),Xs_1))))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
        & hBOOL(hAPP_P1894408759t_bool(Pa,X_2)) ) ) ).

tff(fact_682_set__takeWhileD,axiom,
    ! [X_2: arrow_856714788e_indi,Pa: fun_Ar1809396326i_bool,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(takeWh259024059e_indi(Pa),Xs_1))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
        & hBOOL(hAPP_A997847300i_bool(Pa,X_2)) ) ) ).

tff(fact_683_set__takeWhileD,axiom,
    ! [X_2: bool,Pa: fun_bool_bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(takeWhile_bool(Pa),Xs_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
        & hBOOL(hAPP_bool_bool(Pa,X_2)) ) ) ).

tff(fact_684_set__takeWhileD,axiom,
    ! [X_2: fun_fu2114379172t_bool,Pa: fun_fu2098777574l_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(takeWh1969918523t_bool(Pa),Xs_1))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
        & hBOOL(hAPP_f1572141188l_bool(Pa,X_2)) ) ) ).

tff(fact_685_set__takeWhileD,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Pa: fun_fu638310559l_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(takeWh2085154898t_bool(Pa),Xs_1))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
        & hBOOL(hAPP_f52567537l_bool(Pa,X_2)) ) ) ).

tff(fact_686_set__takeWhileD,axiom,
    ! [X_2: fun_Ar274636406t_bool,Pa: fun_fu3835832l_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(takeWh1481438221t_bool(Pa),Xs_1))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
        & hBOOL(hAPP_f995490902l_bool(Pa,X_2)) ) ) ).

tff(fact_687_set__takeWhileD,axiom,
    ! [X_2: produc472769767le_alt,Pa: fun_Pr2067565481t_bool,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(takeWh1421241214le_alt(Pa),Xs_1))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
        & hBOOL(hAPP_P1178790471t_bool(Pa,X_2)) ) ) ).

tff(fact_688_in__set__butlastD,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,Xs_1))))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) ) ).

tff(fact_689_in__set__butlastD,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_1))))
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1))) ) ).

tff(fact_690_in__set__butlastD,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(butlas1837197275le_alt,Xs_1))))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1))) ) ).

tff(fact_691_in__set__butlastD,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(butlas981234984e_indi,Xs_1))))
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1))) ) ).

tff(fact_692_in__set__butlastD,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,Xs_1))))
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) ) ).

tff(fact_693_in__set__butlastD,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(butlas1125166248t_bool,Xs_1))))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1))) ) ).

tff(fact_694_in__set__butlastD,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(butlas1729912741t_bool,Xs_1))))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1))) ) ).

tff(fact_695_in__set__butlastD,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(butlas481790330t_bool,Xs_1))))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1))) ) ).

tff(fact_696_in__set__butlastD,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(butlas1780591595le_alt,Xs_1))))
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1))) ) ).

tff(fact_697_set__rotate1,axiom,
    ! [Xs_1: list_A114658244le_alt] : ( set_Ar1995755744le_alt(hAPP_l84111627le_alt(rotate1753650700le_alt,Xs_1)) = set_Ar1995755744le_alt(Xs_1) ) ).

tff(fact_698_in__set__insert,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ( hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_699_in__set__insert,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(insert1391384533le_alt,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_700_in__set__insert,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ( hAPP_l922056661le_alt(hAPP_P1680517091le_alt(insert559460497le_alt,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_701_in__set__insert,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ( hAPP_l713773333e_indi(hAPP_A1580343958e_indi(insert901693150e_indi,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_702_in__set__insert,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ( hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_703_in__set__insert,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ( hAPP_l1936976149t_bool(hAPP_f559469846t_bool(insert1598751326t_bool,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_704_in__set__insert,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ( hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(insert774660719t_bool,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_705_in__set__insert,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ( hAPP_l179891349t_bool(hAPP_f994423108t_bool(insert1837816112t_bool,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_706_in__set__insert,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ( hAPP_l1424955733le_alt(hAPP_P437856723le_alt(insert148673953le_alt,X_2),Xs_1) = Xs_1 ) ) ).

tff(fact_707_distinct_Osimps_I2_J,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
        & hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_1)) ) ) ).

tff(fact_708_distinct_Osimps_I2_J,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
        & hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs_1)) ) ) ).

tff(fact_709_distinct_Osimps_I2_J,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_l255772864t_bool(distin1934286196le_alt,hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
        & hBOOL(hAPP_l255772864t_bool(distin1934286196le_alt,Xs_1)) ) ) ).

tff(fact_710_distinct_Osimps_I2_J,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_l311606797i_bool(distin1343912001e_indi,hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
        & hBOOL(hAPP_l311606797i_bool(distin1343912001e_indi,Xs_1)) ) ) ).

tff(fact_711_distinct_Osimps_I2_J,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_list_bool_bool(distinct_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
        & hBOOL(hAPP_list_bool_bool(distinct_bool,Xs_1)) ) ) ).

tff(fact_712_distinct_Osimps_I2_J,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_l1502732685l_bool(distin1644384705t_bool,hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
        & hBOOL(hAPP_l1502732685l_bool(distin1644384705t_bool,Xs_1)) ) ) ).

tff(fact_713_distinct_Osimps_I2_J,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_l1252368702l_bool(distin116221260t_bool,hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
        & hBOOL(hAPP_l1252368702l_bool(distin116221260t_bool,Xs_1)) ) ) ).

tff(fact_714_distinct_Osimps_I2_J,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_l446901855l_bool(distin194731411t_bool,hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
        & hBOOL(hAPP_l446901855l_bool(distin194731411t_bool,Xs_1)) ) ) ).

tff(fact_715_distinct_Osimps_I2_J,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_l423847376t_bool(distin748429060le_alt,hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Xs_1)))
    <=> ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
        & hBOOL(hAPP_l423847376t_bool(distin748429060le_alt,Xs_1)) ) ) ).

tff(fact_716_takeWhile__append1,axiom,
    ! [Ys_1: list_nat,Pa: fun_nat_bool,X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ( ~ hBOOL(hAPP_nat_bool(Pa,X_2))
       => ( hAPP_l248265089st_nat(takeWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(takeWhile_nat(Pa),Xs_1) ) ) ) ).

tff(fact_717_takeWhile__append1,axiom,
    ! [Ys_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ( ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
       => ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1)) = hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Xs_1) ) ) ) ).

tff(fact_718_takeWhile__append1,axiom,
    ! [Ys_1: list_P662130680le_alt,Pa: fun_Pr486337689t_bool,X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ( ~ hBOOL(hAPP_P1894408759t_bool(Pa,X_2))
       => ( hAPP_l922056661le_alt(takeWh797115118le_alt(Pa),hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Xs_1),Ys_1)) = hAPP_l922056661le_alt(takeWh797115118le_alt(Pa),Xs_1) ) ) ) ).

tff(fact_719_takeWhile__append1,axiom,
    ! [Ys_1: list_A270647749e_indi,Pa: fun_Ar1809396326i_bool,X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ( ~ hBOOL(hAPP_A997847300i_bool(Pa,X_2))
       => ( hAPP_l713773333e_indi(takeWh259024059e_indi(Pa),hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Xs_1),Ys_1)) = hAPP_l713773333e_indi(takeWh259024059e_indi(Pa),Xs_1) ) ) ) ).

tff(fact_720_takeWhile__append1,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_bool_bool(Pa,X_2))
       => ( hAPP_l1189022293t_bool(takeWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)) = hAPP_l1189022293t_bool(takeWhile_bool(Pa),Xs_1) ) ) ) ).

tff(fact_721_takeWhile__append1,axiom,
    ! [Ys_1: list_f1981087045t_bool,Pa: fun_fu2098777574l_bool,X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_f1572141188l_bool(Pa,X_2))
       => ( hAPP_l1936976149t_bool(takeWh1969918523t_bool(Pa),hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Xs_1),Ys_1)) = hAPP_l1936976149t_bool(takeWh1969918523t_bool(Pa),Xs_1) ) ) ) ).

tff(fact_722_takeWhile__append1,axiom,
    ! [Ys_1: list_f733367646t_bool,Pa: fun_fu638310559l_bool,X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(Pa,X_2))
       => ( hAPP_l1229506623t_bool(takeWh2085154898t_bool(Pa),hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Xs_1),Ys_1)) = hAPP_l1229506623t_bool(takeWh2085154898t_bool(Pa),Xs_1) ) ) ) ).

tff(fact_723_takeWhile__append1,axiom,
    ! [Ys_1: list_f1976315671t_bool,Pa: fun_fu3835832l_bool,X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_f995490902l_bool(Pa,X_2))
       => ( hAPP_l179891349t_bool(takeWh1481438221t_bool(Pa),hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Xs_1),Ys_1)) = hAPP_l179891349t_bool(takeWh1481438221t_bool(Pa),Xs_1) ) ) ) ).

tff(fact_724_takeWhile__append1,axiom,
    ! [Ys_1: list_P1419683592le_alt,Pa: fun_Pr2067565481t_bool,X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ( ~ hBOOL(hAPP_P1178790471t_bool(Pa,X_2))
       => ( hAPP_l1424955733le_alt(takeWh1421241214le_alt(Pa),hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Xs_1),Ys_1)) = hAPP_l1424955733le_alt(takeWh1421241214le_alt(Pa),Xs_1) ) ) ) ).

tff(fact_725_last__in__set,axiom,
    ! [As: list_A114658244le_alt] :
      ( ( As != nil_Ar557011903le_alt )
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,last_A488133080le_alt(As)),set_Ar1995755744le_alt(As))) ) ).

tff(fact_726_last__in__set,axiom,
    ! [As: list_nat] :
      ( ( As != nil_nat )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,last_nat(As)),set_nat(As))) ) ).

tff(fact_727_last__in__set,axiom,
    ! [As: list_P662130680le_alt] :
      ( ( As != nil_Pr1738530343le_alt )
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,last_P1104483278le_alt(As)),set_Pr1785012934le_alt(As))) ) ).

tff(fact_728_last__in__set,axiom,
    ! [As: list_A270647749e_indi] :
      ( ( As != nil_Ar1954758004e_indi )
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,last_A1878443419e_indi(As)),set_Ar205654163e_indi(As))) ) ).

tff(fact_729_last__in__set,axiom,
    ! [As: list_bool] :
      ( ( As != nil_bool )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,last_bool(As)),set_bool(As))) ) ).

tff(fact_730_last__in__set,axiom,
    ! [As: list_f1981087045t_bool] :
      ( ( As != nil_fu1881361652t_bool )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,last_f1285862171t_bool(As)),set_fu2135320083t_bool(As))) ) ).

tff(fact_731_last__in__set,axiom,
    ! [As: list_f733367646t_bool] :
      ( ( As != nil_fu1079711833t_bool )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,last_f537687922t_bool(As)),set_fu1957445242t_bool(As))) ) ).

tff(fact_732_last__in__set,axiom,
    ! [As: list_f1976315671t_bool] :
      ( ( As != nil_fu2063482310t_bool )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,last_f1589458157t_bool(As)),set_fu2037886949t_bool(As))) ) ).

tff(fact_733_last__in__set,axiom,
    ! [As: list_P1419683592le_alt] :
      ( ( As != nil_Pr1980478519le_alt )
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,last_P628018270le_alt(As)),set_Pr496668502le_alt(As))) ) ).

tff(fact_734_dropWhile__eq__Nil__conv,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1) = nil_Ar557011903le_alt )
    <=> ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
         => hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) ) ) ).

tff(fact_735_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_nat,X_2: nat,Xs_1: list_nat] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,Xs_1))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,Ys_1)))) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1))))) ) ).

tff(fact_736_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_A114658244le_alt,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,Xs_1))))
        | hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,Ys_1)))) )
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1))))) ) ).

tff(fact_737_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_P662130680le_alt,X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(butlas1837197275le_alt,Xs_1))))
        | hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(butlas1837197275le_alt,Ys_1)))) )
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(butlas1837197275le_alt,hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Xs_1),Ys_1))))) ) ).

tff(fact_738_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_A270647749e_indi,X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(butlas981234984e_indi,Xs_1))))
        | hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(butlas981234984e_indi,Ys_1)))) )
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(butlas981234984e_indi,hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Xs_1),Ys_1))))) ) ).

tff(fact_739_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_bool,X_2: bool,Xs_1: list_bool] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,Xs_1))))
        | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,Ys_1)))) )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1))))) ) ).

tff(fact_740_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_f1981087045t_bool,X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(butlas1125166248t_bool,Xs_1))))
        | hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(butlas1125166248t_bool,Ys_1)))) )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(butlas1125166248t_bool,hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Xs_1),Ys_1))))) ) ).

tff(fact_741_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_f733367646t_bool,X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(butlas1729912741t_bool,Xs_1))))
        | hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(butlas1729912741t_bool,Ys_1)))) )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(butlas1729912741t_bool,hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Xs_1),Ys_1))))) ) ).

tff(fact_742_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_f1976315671t_bool,X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(butlas481790330t_bool,Xs_1))))
        | hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(butlas481790330t_bool,Ys_1)))) )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(butlas481790330t_bool,hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Xs_1),Ys_1))))) ) ).

tff(fact_743_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_P1419683592le_alt,X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(butlas1780591595le_alt,Xs_1))))
        | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(butlas1780591595le_alt,Ys_1)))) )
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(butlas1780591595le_alt,hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Xs_1),Ys_1))))) ) ).

tff(fact_744_hd__in__set,axiom,
    ! [Xs_1: list_A114658244le_alt] :
      ( ( Xs_1 != nil_Ar557011903le_alt )
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hd_Arr1236501138le_alt(Xs_1)),set_Ar1995755744le_alt(Xs_1))) ) ).

tff(fact_745_hd__in__set,axiom,
    ! [Xs_1: list_nat] :
      ( ( Xs_1 != nil_nat )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hd_nat(Xs_1)),set_nat(Xs_1))) ) ).

tff(fact_746_hd__in__set,axiom,
    ! [Xs_1: list_P662130680le_alt] :
      ( ( Xs_1 != nil_Pr1738530343le_alt )
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hd_Pro82081940le_alt(Xs_1)),set_Pr1785012934le_alt(Xs_1))) ) ).

tff(fact_747_hd__in__set,axiom,
    ! [Xs_1: list_A270647749e_indi] :
      ( ( Xs_1 != nil_Ar1954758004e_indi )
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hd_Arr451003233e_indi(Xs_1)),set_Ar205654163e_indi(Xs_1))) ) ).

tff(fact_748_hd__in__set,axiom,
    ! [Xs_1: list_bool] :
      ( ( Xs_1 != nil_bool )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hd_bool(Xs_1)),set_bool(Xs_1))) ) ).

tff(fact_749_hd__in__set,axiom,
    ! [Xs_1: list_f1981087045t_bool] :
      ( ( Xs_1 != nil_fu1881361652t_bool )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hd_fun1991171297t_bool(Xs_1)),set_fu2135320083t_bool(Xs_1))) ) ).

tff(fact_750_hd__in__set,axiom,
    ! [Xs_1: list_f733367646t_bool] :
      ( ( Xs_1 != nil_fu1079711833t_bool )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hd_fun1302671916t_bool(Xs_1)),set_fu1957445242t_bool(Xs_1))) ) ).

tff(fact_751_hd__in__set,axiom,
    ! [Xs_1: list_f1976315671t_bool] :
      ( ( Xs_1 != nil_fu2063482310t_bool )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hd_fun449104051t_bool(Xs_1)),set_fu2037886949t_bool(Xs_1))) ) ).

tff(fact_752_hd__in__set,axiom,
    ! [Xs_1: list_P1419683592le_alt] :
      ( ( Xs_1 != nil_Pr1980478519le_alt )
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hd_Pro1416718884le_alt(Xs_1)),set_Pr496668502le_alt(Xs_1))) ) ).

tff(fact_753_dropWhile__append1,axiom,
    ! [Ys_1: list_nat,Pa: fun_nat_bool,X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ( ~ hBOOL(hAPP_nat_bool(Pa,X_2))
       => ( hAPP_l248265089st_nat(dropWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(dropWhile_nat(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_754_dropWhile__append1,axiom,
    ! [Ys_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ( ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_2))
       => ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_755_dropWhile__append1,axiom,
    ! [Ys_1: list_P662130680le_alt,Pa: fun_Pr486337689t_bool,X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ( ~ hBOOL(hAPP_P1894408759t_bool(Pa,X_2))
       => ( hAPP_l922056661le_alt(dropWh1985299526le_alt(Pa),hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Xs_1),Ys_1)) = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,hAPP_l922056661le_alt(dropWh1985299526le_alt(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_756_dropWhile__append1,axiom,
    ! [Ys_1: list_A270647749e_indi,Pa: fun_Ar1809396326i_bool,X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ( ~ hBOOL(hAPP_A997847300i_bool(Pa,X_2))
       => ( hAPP_l713773333e_indi(dropWh587229715e_indi(Pa),hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Xs_1),Ys_1)) = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,hAPP_l713773333e_indi(dropWh587229715e_indi(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_757_dropWhile__append1,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_bool_bool(Pa,X_2))
       => ( hAPP_l1189022293t_bool(dropWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(dropWhile_bool(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_758_dropWhile__append1,axiom,
    ! [Ys_1: list_f1981087045t_bool,Pa: fun_fu2098777574l_bool,X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_f1572141188l_bool(Pa,X_2))
       => ( hAPP_l1936976149t_bool(dropWh1823459219t_bool(Pa),hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Xs_1),Ys_1)) = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,hAPP_l1936976149t_bool(dropWh1823459219t_bool(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_759_dropWhile__append1,axiom,
    ! [Ys_1: list_f733367646t_bool,Pa: fun_fu638310559l_bool,X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(Pa,X_2))
       => ( hAPP_l1229506623t_bool(dropWh1706032378t_bool(Pa),hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Xs_1),Ys_1)) = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,hAPP_l1229506623t_bool(dropWh1706032378t_bool(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_760_dropWhile__append1,axiom,
    ! [Ys_1: list_f1976315671t_bool,Pa: fun_fu3835832l_bool,X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ( ~ hBOOL(hAPP_f995490902l_bool(Pa,X_2))
       => ( hAPP_l179891349t_bool(dropWh1724617061t_bool(Pa),hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Xs_1),Ys_1)) = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,hAPP_l179891349t_bool(dropWh1724617061t_bool(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_761_dropWhile__append1,axiom,
    ! [Ys_1: list_P1419683592le_alt,Pa: fun_Pr2067565481t_bool,X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ( ~ hBOOL(hAPP_P1178790471t_bool(Pa,X_2))
       => ( hAPP_l1424955733le_alt(dropWh1799418070le_alt(Pa),hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Xs_1),Ys_1)) = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,hAPP_l1424955733le_alt(dropWh1799418070le_alt(Pa),Xs_1)),Ys_1) ) ) ) ).

tff(fact_762_List_Oinsert__def,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
       => ( hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
       => ( hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1) ) ) ) ).

tff(fact_763_List_Oinsert__def,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
       => ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(insert1391384533le_alt,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
       => ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(insert1391384533le_alt,X_2),Xs_1) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) ) ) ) ).

tff(fact_764_List_Oinsert__def,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
       => ( hAPP_l922056661le_alt(hAPP_P1680517091le_alt(insert559460497le_alt,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
       => ( hAPP_l922056661le_alt(hAPP_P1680517091le_alt(insert559460497le_alt,X_2),Xs_1) = hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Xs_1) ) ) ) ).

tff(fact_765_List_Oinsert__def,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
       => ( hAPP_l713773333e_indi(hAPP_A1580343958e_indi(insert901693150e_indi,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
       => ( hAPP_l713773333e_indi(hAPP_A1580343958e_indi(insert901693150e_indi,X_2),Xs_1) = hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Xs_1) ) ) ) ).

tff(fact_766_List_Oinsert__def,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
       => ( hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
       => ( hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1) ) ) ) ).

tff(fact_767_List_Oinsert__def,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
       => ( hAPP_l1936976149t_bool(hAPP_f559469846t_bool(insert1598751326t_bool,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
       => ( hAPP_l1936976149t_bool(hAPP_f559469846t_bool(insert1598751326t_bool,X_2),Xs_1) = hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Xs_1) ) ) ) ).

tff(fact_768_List_Oinsert__def,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
       => ( hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(insert774660719t_bool,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
       => ( hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(insert774660719t_bool,X_2),Xs_1) = hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Xs_1) ) ) ) ).

tff(fact_769_List_Oinsert__def,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
       => ( hAPP_l179891349t_bool(hAPP_f994423108t_bool(insert1837816112t_bool,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
       => ( hAPP_l179891349t_bool(hAPP_f994423108t_bool(insert1837816112t_bool,X_2),Xs_1) = hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Xs_1) ) ) ) ).

tff(fact_770_List_Oinsert__def,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
       => ( hAPP_l1424955733le_alt(hAPP_P437856723le_alt(insert148673953le_alt,X_2),Xs_1) = Xs_1 ) )
      & ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
       => ( hAPP_l1424955733le_alt(hAPP_P437856723le_alt(insert148673953le_alt,X_2),Xs_1) = hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Xs_1) ) ) ) ).

tff(fact_771_not__in__set__insert,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ( hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1) ) ) ).

tff(fact_772_not__in__set__insert,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(insert1391384533le_alt,X_2),Xs_1) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1) ) ) ).

tff(fact_773_not__in__set__insert,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ( hAPP_l922056661le_alt(hAPP_P1680517091le_alt(insert559460497le_alt,X_2),Xs_1) = hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Xs_1) ) ) ).

tff(fact_774_not__in__set__insert,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ( hAPP_l713773333e_indi(hAPP_A1580343958e_indi(insert901693150e_indi,X_2),Xs_1) = hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Xs_1) ) ) ).

tff(fact_775_not__in__set__insert,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ( hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1) ) ) ).

tff(fact_776_not__in__set__insert,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ( hAPP_l1936976149t_bool(hAPP_f559469846t_bool(insert1598751326t_bool,X_2),Xs_1) = hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Xs_1) ) ) ).

tff(fact_777_not__in__set__insert,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ( hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(insert774660719t_bool,X_2),Xs_1) = hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Xs_1) ) ) ).

tff(fact_778_not__in__set__insert,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ( hAPP_l179891349t_bool(hAPP_f994423108t_bool(insert1837816112t_bool,X_2),Xs_1) = hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Xs_1) ) ) ).

tff(fact_779_not__in__set__insert,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ( hAPP_l1424955733le_alt(hAPP_P437856723le_alt(insert148673953le_alt,X_2),Xs_1) = hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Xs_1) ) ) ).

tff(fact_780_partition__P,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt,Yes: list_A114658244le_alt,No: list_A114658244le_alt] :
      ( ( partit758395576le_alt(Pa,Xs_1) = hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Yes),No) )
     => ( ! [X_1: arrow_1893660431le_alt] :
            ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Yes)))
           => hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
        & ! [X_1: arrow_1893660431le_alt] :
            ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(No)))
           => ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) ) ) ) ).

tff(fact_781_lexord__partial__trans,axiom,
    ! [Zs_1: list_A114658244le_alt,Ys_1: list_A114658244le_alt,R_2: fun_Pr2067565481t_bool,Xs_1: list_A114658244le_alt] :
      ( ! [X_1: arrow_1893660431le_alt,Y_9: arrow_1893660431le_alt,Z_4: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
         => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Ys_1)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
       => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ys_1),Zs_1)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2)))
         => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xs_1),Zs_1)),hAPP_f369701637t_bool(lexord228913196le_alt,R_2))) ) ) ) ).

tff(fact_782_lexord__partial__trans,axiom,
    ! [Zs_1: list_l2028444773le_alt,Ys_1: list_l2028444773le_alt,R_2: fun_Pr486337689t_bool,Xs_1: list_l2028444773le_alt] :
      ( ! [X_1: list_A114658244le_alt,Y_9: list_A114658244le_alt,Z_4: list_A114658244le_alt] :
          ( hBOOL(hAPP_f1996171982l_bool(hAPP_l1280938307l_bool(member1145038001le_alt,X_1),set_li1778885299le_alt(Xs_1)))
         => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Ys_1)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2)))
       => ( hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Ys_1),Zs_1)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2)))
         => hBOOL(hAPP_f155771121l_bool(hAPP_P2060499849l_bool(member399934036le_alt,hAPP_l571271991le_alt(hAPP_l949242293le_alt(produc48145751le_alt,Xs_1),Zs_1)),hAPP_f417980453t_bool(lexord616819815le_alt,R_2))) ) ) ) ).

tff(fact_783_lexord__partial__trans,axiom,
    ! [Zs_1: list_nat,Ys_1: list_nat,R_2: fun_Pr1927655017t_bool,Xs_1: list_nat] :
      ( ! [X_1: nat,Y_9: nat,Z_4: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(Xs_1)))
         => ( hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f1919691607l_bool(hAPP_P1736545109l_bool(member910422074st_nat,hAPP_l318352527st_nat(hAPP_l1148138287st_nat(produc1869962435st_nat,Xs_1),Ys_1)),hAPP_f29979067t_bool(lexord_nat,R_2)))
       => ( hBOOL(hAPP_f1919691607l_bool(hAPP_P1736545109l_bool(member910422074st_nat,hAPP_l318352527st_nat(hAPP_l1148138287st_nat(produc1869962435st_nat,Ys_1),Zs_1)),hAPP_f29979067t_bool(lexord_nat,R_2)))
         => hBOOL(hAPP_f1919691607l_bool(hAPP_P1736545109l_bool(member910422074st_nat,hAPP_l318352527st_nat(hAPP_l1148138287st_nat(produc1869962435st_nat,Xs_1),Zs_1)),hAPP_f29979067t_bool(lexord_nat,R_2))) ) ) ) ).

tff(fact_784_lexord__partial__trans,axiom,
    ! [Zs_1: list_P662130680le_alt,Ys_1: list_P662130680le_alt,R_2: fun_Pr31738815t_bool,Xs_1: list_P662130680le_alt] :
      ( ! [X_1: produc587761367le_alt,Y_9: produc587761367le_alt,Z_4: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),set_Pr1785012934le_alt(Xs_1)))
         => ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f354949425l_bool(hAPP_P1538717705l_bool(member2130615444le_alt,hAPP_l235329034le_alt(hAPP_l331879323le_alt(produc1238470167le_alt,Xs_1),Ys_1)),hAPP_f2027451327t_bool(lexord198649978le_alt,R_2)))
       => ( hBOOL(hAPP_f354949425l_bool(hAPP_P1538717705l_bool(member2130615444le_alt,hAPP_l235329034le_alt(hAPP_l331879323le_alt(produc1238470167le_alt,Ys_1),Zs_1)),hAPP_f2027451327t_bool(lexord198649978le_alt,R_2)))
         => hBOOL(hAPP_f354949425l_bool(hAPP_P1538717705l_bool(member2130615444le_alt,hAPP_l235329034le_alt(hAPP_l331879323le_alt(produc1238470167le_alt,Xs_1),Zs_1)),hAPP_f2027451327t_bool(lexord198649978le_alt,R_2))) ) ) ) ).

tff(fact_785_lexord__partial__trans,axiom,
    ! [Zs_1: list_A270647749e_indi,Ys_1: list_A270647749e_indi,R_2: fun_Pr140956505i_bool,Xs_1: list_A270647749e_indi] :
      ( ! [X_1: arrow_856714788e_indi,Y_9: arrow_856714788e_indi,Z_4: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),set_Ar205654163e_indi(Xs_1)))
         => ( hBOOL(hAPP_f1031426977l_bool(hAPP_P67597801l_bool(member155382916e_indi,hAPP_A108654910e_indi(hAPP_A1516404665e_indi(produc1408223885e_indi,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f1031426977l_bool(hAPP_P67597801l_bool(member155382916e_indi,hAPP_A108654910e_indi(hAPP_A1516404665e_indi(produc1408223885e_indi,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f1031426977l_bool(hAPP_P67597801l_bool(member155382916e_indi,hAPP_A108654910e_indi(hAPP_A1516404665e_indi(produc1408223885e_indi,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f1678148209l_bool(hAPP_P329666697l_bool(member1257664212e_indi,hAPP_l321397271e_indi(hAPP_l814083573e_indi(produc1006390615e_indi,Xs_1),Ys_1)),hAPP_f1690083045i_bool(lexord1088797767e_indi,R_2)))
       => ( hBOOL(hAPP_f1678148209l_bool(hAPP_P329666697l_bool(member1257664212e_indi,hAPP_l321397271e_indi(hAPP_l814083573e_indi(produc1006390615e_indi,Ys_1),Zs_1)),hAPP_f1690083045i_bool(lexord1088797767e_indi,R_2)))
         => hBOOL(hAPP_f1678148209l_bool(hAPP_P329666697l_bool(member1257664212e_indi,hAPP_l321397271e_indi(hAPP_l814083573e_indi(produc1006390615e_indi,Xs_1),Zs_1)),hAPP_f1690083045i_bool(lexord1088797767e_indi,R_2))) ) ) ) ).

tff(fact_786_lexord__partial__trans,axiom,
    ! [Zs_1: list_bool,Ys_1: list_bool,R_2: fun_Pr754217419l_bool,Xs_1: list_bool] :
      ( ! [X_1: bool,Y_9: bool,Z_4: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs_1)))
         => ( hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs_1),Ys_1)),hAPP_f1114274611l_bool(lexord_bool,R_2)))
       => ( hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Ys_1),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_2)))
         => hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs_1),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_2))) ) ) ) ).

tff(fact_787_lexord__partial__trans,axiom,
    ! [Zs_1: list_f1981087045t_bool,Ys_1: list_f1981087045t_bool,R_2: fun_Pr1885043289l_bool,Xs_1: list_f1981087045t_bool] :
      ( ! [X_1: fun_fu2114379172t_bool,Y_9: fun_fu2114379172t_bool,Z_4: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),set_fu2135320083t_bool(Xs_1)))
         => ( hBOOL(hAPP_f1832307361l_bool(hAPP_P1486810089l_bool(member331044740t_bool,hAPP_f1291584446t_bool(hAPP_f1528586425t_bool(produc857581453t_bool,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f1832307361l_bool(hAPP_P1486810089l_bool(member331044740t_bool,hAPP_f1291584446t_bool(hAPP_f1528586425t_bool(produc857581453t_bool,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f1832307361l_bool(hAPP_P1486810089l_bool(member331044740t_bool,hAPP_f1291584446t_bool(hAPP_f1528586425t_bool(produc857581453t_bool,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f1547577457l_bool(hAPP_P886531209l_bool(member292487380t_bool,hAPP_l2146059159t_bool(hAPP_l559590133t_bool(produc836087127t_bool,Xs_1),Ys_1)),hAPP_f203861477l_bool(lexord1846952391t_bool,R_2)))
       => ( hBOOL(hAPP_f1547577457l_bool(hAPP_P886531209l_bool(member292487380t_bool,hAPP_l2146059159t_bool(hAPP_l559590133t_bool(produc836087127t_bool,Ys_1),Zs_1)),hAPP_f203861477l_bool(lexord1846952391t_bool,R_2)))
         => hBOOL(hAPP_f1547577457l_bool(hAPP_P886531209l_bool(member292487380t_bool,hAPP_l2146059159t_bool(hAPP_l559590133t_bool(produc836087127t_bool,Xs_1),Zs_1)),hAPP_f203861477l_bool(lexord1846952391t_bool,R_2))) ) ) ) ).

tff(fact_788_lexord__partial__trans,axiom,
    ! [Zs_1: list_f733367646t_bool,Ys_1: list_f733367646t_bool,R_2: fun_Pr932490025l_bool,Xs_1: list_f733367646t_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool,Y_9: fun_Pr2067565481t_bool,Z_4: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),set_fu1957445242t_bool(Xs_1)))
         => ( hBOOL(hAPP_f808625521l_bool(hAPP_P1653001865l_bool(member1681679828t_bool,hAPP_f174661371t_bool(hAPP_f1337878717t_bool(produc873875543t_bool,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f808625521l_bool(hAPP_P1653001865l_bool(member1681679828t_bool,hAPP_f174661371t_bool(hAPP_f1337878717t_bool(produc873875543t_bool,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f808625521l_bool(hAPP_P1653001865l_bool(member1681679828t_bool,hAPP_f174661371t_bool(hAPP_f1337878717t_bool(produc873875543t_bool,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f582070293l_bool(hAPP_P563751121l_bool(member2002415608t_bool,hAPP_l1900989676t_bool(hAPP_l315980333t_bool(produc2021583233t_bool,Xs_1),Ys_1)),hAPP_f93904057l_bool(lexord1057491398t_bool,R_2)))
       => ( hBOOL(hAPP_f582070293l_bool(hAPP_P563751121l_bool(member2002415608t_bool,hAPP_l1900989676t_bool(hAPP_l315980333t_bool(produc2021583233t_bool,Ys_1),Zs_1)),hAPP_f93904057l_bool(lexord1057491398t_bool,R_2)))
         => hBOOL(hAPP_f582070293l_bool(hAPP_P563751121l_bool(member2002415608t_bool,hAPP_l1900989676t_bool(hAPP_l315980333t_bool(produc2021583233t_bool,Xs_1),Zs_1)),hAPP_f93904057l_bool(lexord1057491398t_bool,R_2))) ) ) ) ).

tff(fact_789_lexord__partial__trans,axiom,
    ! [Zs_1: list_f1976315671t_bool,Ys_1: list_f1976315671t_bool,R_2: fun_Pr1677349629l_bool,Xs_1: list_f1976315671t_bool] :
      ( ! [X_1: fun_Ar274636406t_bool,Y_9: fun_Ar274636406t_bool,Z_4: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),set_fu2037886949t_bool(Xs_1)))
         => ( hBOOL(hAPP_f265509189l_bool(hAPP_P53043505l_bool(member565818408t_bool,hAPP_f876036148t_bool(hAPP_f970649309t_bool(produc148697137t_bool,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f265509189l_bool(hAPP_P53043505l_bool(member565818408t_bool,hAPP_f876036148t_bool(hAPP_f970649309t_bool(produc148697137t_bool,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f265509189l_bool(hAPP_P53043505l_bool(member565818408t_bool,hAPP_f876036148t_bool(hAPP_f970649309t_bool(produc148697137t_bool,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f612957169l_bool(hAPP_P1143334793l_bool(member2134761044t_bool,hAPP_l905633001t_bool(hAPP_l197476889t_bool(produc1633570007t_bool,Xs_1),Ys_1)),hAPP_f1168976833l_bool(lexord41383833t_bool,R_2)))
       => ( hBOOL(hAPP_f612957169l_bool(hAPP_P1143334793l_bool(member2134761044t_bool,hAPP_l905633001t_bool(hAPP_l197476889t_bool(produc1633570007t_bool,Ys_1),Zs_1)),hAPP_f1168976833l_bool(lexord41383833t_bool,R_2)))
         => hBOOL(hAPP_f612957169l_bool(hAPP_P1143334793l_bool(member2134761044t_bool,hAPP_l905633001t_bool(hAPP_l197476889t_bool(produc1633570007t_bool,Xs_1),Zs_1)),hAPP_f1168976833l_bool(lexord41383833t_bool,R_2))) ) ) ) ).

tff(fact_790_lexord__partial__trans,axiom,
    ! [Zs_1: list_P1419683592le_alt,Ys_1: list_P1419683592le_alt,R_2: fun_Pr773225055t_bool,Xs_1: list_P1419683592le_alt] :
      ( ! [X_1: produc472769767le_alt,Y_9: produc472769767le_alt,Z_4: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),set_Pr496668502le_alt(Xs_1)))
         => ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,X_1),Y_9)),R_2))
           => ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,Y_9),Z_4)),R_2))
             => hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,X_1),Z_4)),R_2)) ) ) )
     => ( hBOOL(hAPP_f615328049l_bool(hAPP_P641400329l_bool(member828077460le_alt,hAPP_l1149277722le_alt(hAPP_l48758843le_alt(produc214947223le_alt,Xs_1),Ys_1)),hAPP_f1695872799t_bool(lexord1620771594le_alt,R_2)))
       => ( hBOOL(hAPP_f615328049l_bool(hAPP_P641400329l_bool(member828077460le_alt,hAPP_l1149277722le_alt(hAPP_l48758843le_alt(produc214947223le_alt,Ys_1),Zs_1)),hAPP_f1695872799t_bool(lexord1620771594le_alt,R_2)))
         => hBOOL(hAPP_f615328049l_bool(hAPP_P641400329l_bool(member828077460le_alt,hAPP_l1149277722le_alt(hAPP_l48758843le_alt(produc214947223le_alt,Xs_1),Zs_1)),hAPP_f1695872799t_bool(lexord1620771594le_alt,R_2))) ) ) ) ).

tff(fact_791_dropWhile__append2,axiom,
    ! [Ys_1: list_nat,Pa: fun_nat_bool,Xs_1: list_nat] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(Xs_1)))
         => hBOOL(hAPP_nat_bool(Pa,X_1)) )
     => ( hAPP_l248265089st_nat(dropWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(dropWhile_nat(Pa),Ys_1) ) ) ).

tff(fact_792_dropWhile__append2,axiom,
    ! [Ys_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
         => hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1)) = hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),Ys_1) ) ) ).

tff(fact_793_dropWhile__append2,axiom,
    ! [Ys_1: list_P662130680le_alt,Pa: fun_Pr486337689t_bool,Xs_1: list_P662130680le_alt] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),set_Pr1785012934le_alt(Xs_1)))
         => hBOOL(hAPP_P1894408759t_bool(Pa,X_1)) )
     => ( hAPP_l922056661le_alt(dropWh1985299526le_alt(Pa),hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Xs_1),Ys_1)) = hAPP_l922056661le_alt(dropWh1985299526le_alt(Pa),Ys_1) ) ) ).

tff(fact_794_dropWhile__append2,axiom,
    ! [Ys_1: list_A270647749e_indi,Pa: fun_Ar1809396326i_bool,Xs_1: list_A270647749e_indi] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),set_Ar205654163e_indi(Xs_1)))
         => hBOOL(hAPP_A997847300i_bool(Pa,X_1)) )
     => ( hAPP_l713773333e_indi(dropWh587229715e_indi(Pa),hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Xs_1),Ys_1)) = hAPP_l713773333e_indi(dropWh587229715e_indi(Pa),Ys_1) ) ) ).

tff(fact_795_dropWhile__append2,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,Xs_1: list_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs_1)))
         => hBOOL(hAPP_bool_bool(Pa,X_1)) )
     => ( hAPP_l1189022293t_bool(dropWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)) = hAPP_l1189022293t_bool(dropWhile_bool(Pa),Ys_1) ) ) ).

tff(fact_796_dropWhile__append2,axiom,
    ! [Ys_1: list_f1981087045t_bool,Pa: fun_fu2098777574l_bool,Xs_1: list_f1981087045t_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),set_fu2135320083t_bool(Xs_1)))
         => hBOOL(hAPP_f1572141188l_bool(Pa,X_1)) )
     => ( hAPP_l1936976149t_bool(dropWh1823459219t_bool(Pa),hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Xs_1),Ys_1)) = hAPP_l1936976149t_bool(dropWh1823459219t_bool(Pa),Ys_1) ) ) ).

tff(fact_797_dropWhile__append2,axiom,
    ! [Ys_1: list_f733367646t_bool,Pa: fun_fu638310559l_bool,Xs_1: list_f733367646t_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),set_fu1957445242t_bool(Xs_1)))
         => hBOOL(hAPP_f52567537l_bool(Pa,X_1)) )
     => ( hAPP_l1229506623t_bool(dropWh1706032378t_bool(Pa),hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Xs_1),Ys_1)) = hAPP_l1229506623t_bool(dropWh1706032378t_bool(Pa),Ys_1) ) ) ).

tff(fact_798_dropWhile__append2,axiom,
    ! [Ys_1: list_f1976315671t_bool,Pa: fun_fu3835832l_bool,Xs_1: list_f1976315671t_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),set_fu2037886949t_bool(Xs_1)))
         => hBOOL(hAPP_f995490902l_bool(Pa,X_1)) )
     => ( hAPP_l179891349t_bool(dropWh1724617061t_bool(Pa),hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Xs_1),Ys_1)) = hAPP_l179891349t_bool(dropWh1724617061t_bool(Pa),Ys_1) ) ) ).

tff(fact_799_dropWhile__append2,axiom,
    ! [Ys_1: list_P1419683592le_alt,Pa: fun_Pr2067565481t_bool,Xs_1: list_P1419683592le_alt] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),set_Pr496668502le_alt(Xs_1)))
         => hBOOL(hAPP_P1178790471t_bool(Pa,X_1)) )
     => ( hAPP_l1424955733le_alt(dropWh1799418070le_alt(Pa),hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Xs_1),Ys_1)) = hAPP_l1424955733le_alt(dropWh1799418070le_alt(Pa),Ys_1) ) ) ).

tff(fact_800_takeWhile__append2,axiom,
    ! [Ys_1: list_nat,Pa: fun_nat_bool,Xs_1: list_nat] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(Xs_1)))
         => hBOOL(hAPP_nat_bool(Pa,X_1)) )
     => ( hAPP_l248265089st_nat(takeWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),hAPP_l248265089st_nat(takeWhile_nat(Pa),Ys_1)) ) ) ).

tff(fact_801_takeWhile__append2,axiom,
    ! [Ys_1: list_A114658244le_alt,Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ! [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
         => hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),Ys_1)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Xs_1),hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),Ys_1)) ) ) ).

tff(fact_802_takeWhile__append2,axiom,
    ! [Ys_1: list_P662130680le_alt,Pa: fun_Pr486337689t_bool,Xs_1: list_P662130680le_alt] :
      ( ! [X_1: produc587761367le_alt] :
          ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),set_Pr1785012934le_alt(Xs_1)))
         => hBOOL(hAPP_P1894408759t_bool(Pa,X_1)) )
     => ( hAPP_l922056661le_alt(takeWh797115118le_alt(Pa),hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Xs_1),Ys_1)) = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Xs_1),hAPP_l922056661le_alt(takeWh797115118le_alt(Pa),Ys_1)) ) ) ).

tff(fact_803_takeWhile__append2,axiom,
    ! [Ys_1: list_A270647749e_indi,Pa: fun_Ar1809396326i_bool,Xs_1: list_A270647749e_indi] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),set_Ar205654163e_indi(Xs_1)))
         => hBOOL(hAPP_A997847300i_bool(Pa,X_1)) )
     => ( hAPP_l713773333e_indi(takeWh259024059e_indi(Pa),hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Xs_1),Ys_1)) = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Xs_1),hAPP_l713773333e_indi(takeWh259024059e_indi(Pa),Ys_1)) ) ) ).

tff(fact_804_takeWhile__append2,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,Xs_1: list_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs_1)))
         => hBOOL(hAPP_bool_bool(Pa,X_1)) )
     => ( hAPP_l1189022293t_bool(takeWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),hAPP_l1189022293t_bool(takeWhile_bool(Pa),Ys_1)) ) ) ).

tff(fact_805_takeWhile__append2,axiom,
    ! [Ys_1: list_f1981087045t_bool,Pa: fun_fu2098777574l_bool,Xs_1: list_f1981087045t_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),set_fu2135320083t_bool(Xs_1)))
         => hBOOL(hAPP_f1572141188l_bool(Pa,X_1)) )
     => ( hAPP_l1936976149t_bool(takeWh1969918523t_bool(Pa),hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Xs_1),Ys_1)) = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Xs_1),hAPP_l1936976149t_bool(takeWh1969918523t_bool(Pa),Ys_1)) ) ) ).

tff(fact_806_takeWhile__append2,axiom,
    ! [Ys_1: list_f733367646t_bool,Pa: fun_fu638310559l_bool,Xs_1: list_f733367646t_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),set_fu1957445242t_bool(Xs_1)))
         => hBOOL(hAPP_f52567537l_bool(Pa,X_1)) )
     => ( hAPP_l1229506623t_bool(takeWh2085154898t_bool(Pa),hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Xs_1),Ys_1)) = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Xs_1),hAPP_l1229506623t_bool(takeWh2085154898t_bool(Pa),Ys_1)) ) ) ).

tff(fact_807_takeWhile__append2,axiom,
    ! [Ys_1: list_f1976315671t_bool,Pa: fun_fu3835832l_bool,Xs_1: list_f1976315671t_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),set_fu2037886949t_bool(Xs_1)))
         => hBOOL(hAPP_f995490902l_bool(Pa,X_1)) )
     => ( hAPP_l179891349t_bool(takeWh1481438221t_bool(Pa),hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Xs_1),Ys_1)) = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Xs_1),hAPP_l179891349t_bool(takeWh1481438221t_bool(Pa),Ys_1)) ) ) ).

tff(fact_808_takeWhile__append2,axiom,
    ! [Ys_1: list_P1419683592le_alt,Pa: fun_Pr2067565481t_bool,Xs_1: list_P1419683592le_alt] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),set_Pr496668502le_alt(Xs_1)))
         => hBOOL(hAPP_P1178790471t_bool(Pa,X_1)) )
     => ( hAPP_l1424955733le_alt(takeWh1421241214le_alt(Pa),hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Xs_1),Ys_1)) = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Xs_1),hAPP_l1424955733le_alt(takeWh1421241214le_alt(Pa),Ys_1)) ) ) ).

tff(fact_809_split__list__propE,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ~ ! [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt] :
            ( ? [Zs: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
           => ~ hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) ) ) ).

tff(fact_810_in__set__conv__decomp__first,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
    <=> ? [Ys: list_nat,Zs: list_nat] :
          ( ( Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) )
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Ys))) ) ) ).

tff(fact_811_in__set__conv__decomp__first,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
    <=> ? [Ys: list_A114658244le_alt,Zs: list_A114658244le_alt] :
          ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Ys))) ) ) ).

tff(fact_812_in__set__conv__decomp__first,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
    <=> ? [Ys: list_P662130680le_alt,Zs: list_P662130680le_alt] :
          ( ( Xs_1 = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Ys),hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Ys))) ) ) ).

tff(fact_813_in__set__conv__decomp__first,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
    <=> ? [Ys: list_A270647749e_indi,Zs: list_A270647749e_indi] :
          ( ( Xs_1 = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Ys),hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Zs)) )
          & ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Ys))) ) ) ).

tff(fact_814_in__set__conv__decomp__first,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
    <=> ? [Ys: list_bool,Zs: list_bool] :
          ( ( Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Ys))) ) ) ).

tff(fact_815_in__set__conv__decomp__first,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
    <=> ? [Ys: list_f1981087045t_bool,Zs: list_f1981087045t_bool] :
          ( ( Xs_1 = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Ys),hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Ys))) ) ) ).

tff(fact_816_in__set__conv__decomp__first,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
    <=> ? [Ys: list_f733367646t_bool,Zs: list_f733367646t_bool] :
          ( ( Xs_1 = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Ys),hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Ys))) ) ) ).

tff(fact_817_in__set__conv__decomp__first,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
    <=> ? [Ys: list_f1976315671t_bool,Zs: list_f1976315671t_bool] :
          ( ( Xs_1 = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Ys),hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Ys))) ) ) ).

tff(fact_818_in__set__conv__decomp__first,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
    <=> ? [Ys: list_P1419683592le_alt,Zs: list_P1419683592le_alt] :
          ( ( Xs_1 = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Ys),hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Ys))) ) ) ).

tff(fact_819_in__set__conv__decomp__last,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
    <=> ? [Ys: list_nat,Zs: list_nat] :
          ( ( Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) )
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Zs))) ) ) ).

tff(fact_820_in__set__conv__decomp__last,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
    <=> ? [Ys: list_A114658244le_alt,Zs: list_A114658244le_alt] :
          ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Zs))) ) ) ).

tff(fact_821_in__set__conv__decomp__last,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
    <=> ? [Ys: list_P662130680le_alt,Zs: list_P662130680le_alt] :
          ( ( Xs_1 = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Ys),hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Zs))) ) ) ).

tff(fact_822_in__set__conv__decomp__last,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
    <=> ? [Ys: list_A270647749e_indi,Zs: list_A270647749e_indi] :
          ( ( Xs_1 = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Ys),hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Zs)) )
          & ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Zs))) ) ) ).

tff(fact_823_in__set__conv__decomp__last,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
    <=> ? [Ys: list_bool,Zs: list_bool] :
          ( ( Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Zs))) ) ) ).

tff(fact_824_in__set__conv__decomp__last,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
    <=> ? [Ys: list_f1981087045t_bool,Zs: list_f1981087045t_bool] :
          ( ( Xs_1 = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Ys),hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Zs))) ) ) ).

tff(fact_825_in__set__conv__decomp__last,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
    <=> ? [Ys: list_f733367646t_bool,Zs: list_f733367646t_bool] :
          ( ( Xs_1 = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Ys),hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Zs))) ) ) ).

tff(fact_826_in__set__conv__decomp__last,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
    <=> ? [Ys: list_f1976315671t_bool,Zs: list_f1976315671t_bool] :
          ( ( Xs_1 = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Ys),hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Zs))) ) ) ).

tff(fact_827_in__set__conv__decomp__last,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
    <=> ? [Ys: list_P1419683592le_alt,Zs: list_P1419683592le_alt] :
          ( ( Xs_1 = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Ys),hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Zs))) ) ) ).

tff(fact_828_in__set__conv__decomp,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
    <=> ? [Ys: list_nat,Zs: list_nat] : ( Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) ) ) ).

tff(fact_829_in__set__conv__decomp,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
    <=> ? [Ys: list_A114658244le_alt,Zs: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs)) ) ) ).

tff(fact_830_in__set__conv__decomp,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
    <=> ? [Ys: list_P662130680le_alt,Zs: list_P662130680le_alt] : ( Xs_1 = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Ys),hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Zs)) ) ) ).

tff(fact_831_in__set__conv__decomp,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
    <=> ? [Ys: list_A270647749e_indi,Zs: list_A270647749e_indi] : ( Xs_1 = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Ys),hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Zs)) ) ) ).

tff(fact_832_in__set__conv__decomp,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
    <=> ? [Ys: list_bool,Zs: list_bool] : ( Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) ) ) ).

tff(fact_833_in__set__conv__decomp,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
    <=> ? [Ys: list_f1981087045t_bool,Zs: list_f1981087045t_bool] : ( Xs_1 = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Ys),hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Zs)) ) ) ).

tff(fact_834_in__set__conv__decomp,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
    <=> ? [Ys: list_f733367646t_bool,Zs: list_f733367646t_bool] : ( Xs_1 = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Ys),hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Zs)) ) ) ).

tff(fact_835_in__set__conv__decomp,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
    <=> ? [Ys: list_f1976315671t_bool,Zs: list_f1976315671t_bool] : ( Xs_1 = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Ys),hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Zs)) ) ) ).

tff(fact_836_in__set__conv__decomp,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
    <=> ? [Ys: list_P1419683592le_alt,Zs: list_P1419683592le_alt] : ( Xs_1 = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Ys),hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Zs)) ) ) ).

tff(fact_837_dropWhile__cong,axiom,
    ! [Q_1: fun_nat_bool,Pa: fun_nat_bool,L_1: list_nat,K: list_nat] :
      ( ( L_1 = K )
     => ( ! [X_1: nat] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(L_1)))
           => ( hBOOL(hAPP_nat_bool(Pa,X_1))
            <=> hBOOL(hAPP_nat_bool(Q_1,X_1)) ) )
       => ( hAPP_l248265089st_nat(dropWhile_nat(Pa),L_1) = hAPP_l248265089st_nat(dropWhile_nat(Q_1),K) ) ) ) ).

tff(fact_838_dropWhile__cong,axiom,
    ! [Q_1: fun_Ar17477381t_bool,Pa: fun_Ar17477381t_bool,L_1: list_A114658244le_alt,K: list_A114658244le_alt] :
      ( ( L_1 = K )
     => ( ! [X_1: arrow_1893660431le_alt] :
            ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(L_1)))
           => ( hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
            <=> hBOOL(hAPP_A1748732503t_bool(Q_1,X_1)) ) )
       => ( hAPP_l84111627le_alt(dropWh587599712le_alt(Pa),L_1) = hAPP_l84111627le_alt(dropWh587599712le_alt(Q_1),K) ) ) ) ).

tff(fact_839_dropWhile__cong,axiom,
    ! [Q_1: fun_Pr486337689t_bool,Pa: fun_Pr486337689t_bool,L_1: list_P662130680le_alt,K: list_P662130680le_alt] :
      ( ( L_1 = K )
     => ( ! [X_1: produc587761367le_alt] :
            ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),set_Pr1785012934le_alt(L_1)))
           => ( hBOOL(hAPP_P1894408759t_bool(Pa,X_1))
            <=> hBOOL(hAPP_P1894408759t_bool(Q_1,X_1)) ) )
       => ( hAPP_l922056661le_alt(dropWh1985299526le_alt(Pa),L_1) = hAPP_l922056661le_alt(dropWh1985299526le_alt(Q_1),K) ) ) ) ).

tff(fact_840_dropWhile__cong,axiom,
    ! [Q_1: fun_Ar1809396326i_bool,Pa: fun_Ar1809396326i_bool,L_1: list_A270647749e_indi,K: list_A270647749e_indi] :
      ( ( L_1 = K )
     => ( ! [X_1: arrow_856714788e_indi] :
            ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),set_Ar205654163e_indi(L_1)))
           => ( hBOOL(hAPP_A997847300i_bool(Pa,X_1))
            <=> hBOOL(hAPP_A997847300i_bool(Q_1,X_1)) ) )
       => ( hAPP_l713773333e_indi(dropWh587229715e_indi(Pa),L_1) = hAPP_l713773333e_indi(dropWh587229715e_indi(Q_1),K) ) ) ) ).

tff(fact_841_dropWhile__cong,axiom,
    ! [Q_1: fun_bool_bool,Pa: fun_bool_bool,L_1: list_bool,K: list_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: bool] :
            ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(L_1)))
           => ( hBOOL(hAPP_bool_bool(Pa,X_1))
            <=> hBOOL(hAPP_bool_bool(Q_1,X_1)) ) )
       => ( hAPP_l1189022293t_bool(dropWhile_bool(Pa),L_1) = hAPP_l1189022293t_bool(dropWhile_bool(Q_1),K) ) ) ) ).

tff(fact_842_dropWhile__cong,axiom,
    ! [Q_1: fun_fu2098777574l_bool,Pa: fun_fu2098777574l_bool,L_1: list_f1981087045t_bool,K: list_f1981087045t_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: fun_fu2114379172t_bool] :
            ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),set_fu2135320083t_bool(L_1)))
           => ( hBOOL(hAPP_f1572141188l_bool(Pa,X_1))
            <=> hBOOL(hAPP_f1572141188l_bool(Q_1,X_1)) ) )
       => ( hAPP_l1936976149t_bool(dropWh1823459219t_bool(Pa),L_1) = hAPP_l1936976149t_bool(dropWh1823459219t_bool(Q_1),K) ) ) ) ).

tff(fact_843_dropWhile__cong,axiom,
    ! [Q_1: fun_fu638310559l_bool,Pa: fun_fu638310559l_bool,L_1: list_f733367646t_bool,K: list_f733367646t_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: fun_Pr2067565481t_bool] :
            ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),set_fu1957445242t_bool(L_1)))
           => ( hBOOL(hAPP_f52567537l_bool(Pa,X_1))
            <=> hBOOL(hAPP_f52567537l_bool(Q_1,X_1)) ) )
       => ( hAPP_l1229506623t_bool(dropWh1706032378t_bool(Pa),L_1) = hAPP_l1229506623t_bool(dropWh1706032378t_bool(Q_1),K) ) ) ) ).

tff(fact_844_dropWhile__cong,axiom,
    ! [Q_1: fun_fu3835832l_bool,Pa: fun_fu3835832l_bool,L_1: list_f1976315671t_bool,K: list_f1976315671t_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: fun_Ar274636406t_bool] :
            ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),set_fu2037886949t_bool(L_1)))
           => ( hBOOL(hAPP_f995490902l_bool(Pa,X_1))
            <=> hBOOL(hAPP_f995490902l_bool(Q_1,X_1)) ) )
       => ( hAPP_l179891349t_bool(dropWh1724617061t_bool(Pa),L_1) = hAPP_l179891349t_bool(dropWh1724617061t_bool(Q_1),K) ) ) ) ).

tff(fact_845_dropWhile__cong,axiom,
    ! [Q_1: fun_Pr2067565481t_bool,Pa: fun_Pr2067565481t_bool,L_1: list_P1419683592le_alt,K: list_P1419683592le_alt] :
      ( ( L_1 = K )
     => ( ! [X_1: produc472769767le_alt] :
            ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),set_Pr496668502le_alt(L_1)))
           => ( hBOOL(hAPP_P1178790471t_bool(Pa,X_1))
            <=> hBOOL(hAPP_P1178790471t_bool(Q_1,X_1)) ) )
       => ( hAPP_l1424955733le_alt(dropWh1799418070le_alt(Pa),L_1) = hAPP_l1424955733le_alt(dropWh1799418070le_alt(Q_1),K) ) ) ) ).

tff(fact_846_takeWhile__cong,axiom,
    ! [Q_1: fun_nat_bool,Pa: fun_nat_bool,L_1: list_nat,K: list_nat] :
      ( ( L_1 = K )
     => ( ! [X_1: nat] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(L_1)))
           => ( hBOOL(hAPP_nat_bool(Pa,X_1))
            <=> hBOOL(hAPP_nat_bool(Q_1,X_1)) ) )
       => ( hAPP_l248265089st_nat(takeWhile_nat(Pa),L_1) = hAPP_l248265089st_nat(takeWhile_nat(Q_1),K) ) ) ) ).

tff(fact_847_takeWhile__cong,axiom,
    ! [Q_1: fun_Ar17477381t_bool,Pa: fun_Ar17477381t_bool,L_1: list_A114658244le_alt,K: list_A114658244le_alt] :
      ( ( L_1 = K )
     => ( ! [X_1: arrow_1893660431le_alt] :
            ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(L_1)))
           => ( hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
            <=> hBOOL(hAPP_A1748732503t_bool(Q_1,X_1)) ) )
       => ( hAPP_l84111627le_alt(takeWh967109304le_alt(Pa),L_1) = hAPP_l84111627le_alt(takeWh967109304le_alt(Q_1),K) ) ) ) ).

tff(fact_848_takeWhile__cong,axiom,
    ! [Q_1: fun_Pr486337689t_bool,Pa: fun_Pr486337689t_bool,L_1: list_P662130680le_alt,K: list_P662130680le_alt] :
      ( ( L_1 = K )
     => ( ! [X_1: produc587761367le_alt] :
            ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_1),set_Pr1785012934le_alt(L_1)))
           => ( hBOOL(hAPP_P1894408759t_bool(Pa,X_1))
            <=> hBOOL(hAPP_P1894408759t_bool(Q_1,X_1)) ) )
       => ( hAPP_l922056661le_alt(takeWh797115118le_alt(Pa),L_1) = hAPP_l922056661le_alt(takeWh797115118le_alt(Q_1),K) ) ) ) ).

tff(fact_849_takeWhile__cong,axiom,
    ! [Q_1: fun_Ar1809396326i_bool,Pa: fun_Ar1809396326i_bool,L_1: list_A270647749e_indi,K: list_A270647749e_indi] :
      ( ( L_1 = K )
     => ( ! [X_1: arrow_856714788e_indi] :
            ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),set_Ar205654163e_indi(L_1)))
           => ( hBOOL(hAPP_A997847300i_bool(Pa,X_1))
            <=> hBOOL(hAPP_A997847300i_bool(Q_1,X_1)) ) )
       => ( hAPP_l713773333e_indi(takeWh259024059e_indi(Pa),L_1) = hAPP_l713773333e_indi(takeWh259024059e_indi(Q_1),K) ) ) ) ).

tff(fact_850_takeWhile__cong,axiom,
    ! [Q_1: fun_bool_bool,Pa: fun_bool_bool,L_1: list_bool,K: list_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: bool] :
            ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(L_1)))
           => ( hBOOL(hAPP_bool_bool(Pa,X_1))
            <=> hBOOL(hAPP_bool_bool(Q_1,X_1)) ) )
       => ( hAPP_l1189022293t_bool(takeWhile_bool(Pa),L_1) = hAPP_l1189022293t_bool(takeWhile_bool(Q_1),K) ) ) ) ).

tff(fact_851_takeWhile__cong,axiom,
    ! [Q_1: fun_fu2098777574l_bool,Pa: fun_fu2098777574l_bool,L_1: list_f1981087045t_bool,K: list_f1981087045t_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: fun_fu2114379172t_bool] :
            ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),set_fu2135320083t_bool(L_1)))
           => ( hBOOL(hAPP_f1572141188l_bool(Pa,X_1))
            <=> hBOOL(hAPP_f1572141188l_bool(Q_1,X_1)) ) )
       => ( hAPP_l1936976149t_bool(takeWh1969918523t_bool(Pa),L_1) = hAPP_l1936976149t_bool(takeWh1969918523t_bool(Q_1),K) ) ) ) ).

tff(fact_852_takeWhile__cong,axiom,
    ! [Q_1: fun_fu638310559l_bool,Pa: fun_fu638310559l_bool,L_1: list_f733367646t_bool,K: list_f733367646t_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: fun_Pr2067565481t_bool] :
            ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),set_fu1957445242t_bool(L_1)))
           => ( hBOOL(hAPP_f52567537l_bool(Pa,X_1))
            <=> hBOOL(hAPP_f52567537l_bool(Q_1,X_1)) ) )
       => ( hAPP_l1229506623t_bool(takeWh2085154898t_bool(Pa),L_1) = hAPP_l1229506623t_bool(takeWh2085154898t_bool(Q_1),K) ) ) ) ).

tff(fact_853_takeWhile__cong,axiom,
    ! [Q_1: fun_fu3835832l_bool,Pa: fun_fu3835832l_bool,L_1: list_f1976315671t_bool,K: list_f1976315671t_bool] :
      ( ( L_1 = K )
     => ( ! [X_1: fun_Ar274636406t_bool] :
            ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),set_fu2037886949t_bool(L_1)))
           => ( hBOOL(hAPP_f995490902l_bool(Pa,X_1))
            <=> hBOOL(hAPP_f995490902l_bool(Q_1,X_1)) ) )
       => ( hAPP_l179891349t_bool(takeWh1481438221t_bool(Pa),L_1) = hAPP_l179891349t_bool(takeWh1481438221t_bool(Q_1),K) ) ) ) ).

tff(fact_854_takeWhile__cong,axiom,
    ! [Q_1: fun_Pr2067565481t_bool,Pa: fun_Pr2067565481t_bool,L_1: list_P1419683592le_alt,K: list_P1419683592le_alt] :
      ( ( L_1 = K )
     => ( ! [X_1: produc472769767le_alt] :
            ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),set_Pr496668502le_alt(L_1)))
           => ( hBOOL(hAPP_P1178790471t_bool(Pa,X_1))
            <=> hBOOL(hAPP_P1178790471t_bool(Q_1,X_1)) ) )
       => ( hAPP_l1424955733le_alt(takeWh1421241214le_alt(Pa),L_1) = hAPP_l1424955733le_alt(takeWh1421241214le_alt(Q_1),K) ) ) ) ).

tff(fact_855_rtrancl__induct,axiom,
    ! [Pa: fun_li1109619974t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),transi1124010071le_alt(R_2)))
     => ( hBOOL(hAPP_l499746980t_bool(Pa,Aa))
       => ( ! [Y_9: list_A114658244le_alt,Z_4: list_A114658244le_alt] :
              ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Y_9)),transi1124010071le_alt(R_2)))
             => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_9),Z_4)),R_2))
               => ( hBOOL(hAPP_l499746980t_bool(Pa,Y_9))
                 => hBOOL(hAPP_l499746980t_bool(Pa,Z_4)) ) ) )
         => hBOOL(hAPP_l499746980t_bool(Pa,Ba)) ) ) ) ).

tff(fact_856_rtrancl__induct,axiom,
    ! [Pa: fun_Ar17477381t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),transi1687363644le_alt(R_2)))
     => ( hBOOL(hAPP_A1748732503t_bool(Pa,Aa))
       => ( ! [Y_9: arrow_1893660431le_alt,Z_4: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Y_9)),transi1687363644le_alt(R_2)))
             => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_9),Z_4)),R_2))
               => ( hBOOL(hAPP_A1748732503t_bool(Pa,Y_9))
                 => hBOOL(hAPP_A1748732503t_bool(Pa,Z_4)) ) ) )
         => hBOOL(hAPP_A1748732503t_bool(Pa,Ba)) ) ) ) ).

tff(fact_857_converse__rtrancl__induct,axiom,
    ! [Pa: fun_li1109619974t_bool,Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),transi1124010071le_alt(R_2)))
     => ( hBOOL(hAPP_l499746980t_bool(Pa,Ba))
       => ( ! [Y_9: list_A114658244le_alt,Z_4: list_A114658244le_alt] :
              ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_9),Z_4)),R_2))
             => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Z_4),Ba)),transi1124010071le_alt(R_2)))
               => ( hBOOL(hAPP_l499746980t_bool(Pa,Z_4))
                 => hBOOL(hAPP_l499746980t_bool(Pa,Y_9)) ) ) )
         => hBOOL(hAPP_l499746980t_bool(Pa,Aa)) ) ) ) ).

tff(fact_858_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Ar17477381t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),transi1687363644le_alt(R_2)))
     => ( hBOOL(hAPP_A1748732503t_bool(Pa,Ba))
       => ( ! [Y_9: arrow_1893660431le_alt,Z_4: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_9),Z_4)),R_2))
             => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Z_4),Ba)),transi1687363644le_alt(R_2)))
               => ( hBOOL(hAPP_A1748732503t_bool(Pa,Z_4))
                 => hBOOL(hAPP_A1748732503t_bool(Pa,Y_9)) ) ) )
         => hBOOL(hAPP_A1748732503t_bool(Pa,Aa)) ) ) ) ).

tff(fact_859_converse__rtranclE,axiom,
    ! [X_2: list_A114658244le_alt,Z_3: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Z_3)),transi1124010071le_alt(R_2)))
     => ( ( X_2 != Z_3 )
       => ~ ! [Y_9: list_A114658244le_alt] :
              ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,X_2),Y_9)),R_2))
             => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_9),Z_3)),transi1124010071le_alt(R_2))) ) ) ) ).

tff(fact_860_converse__rtranclE,axiom,
    ! [X_2: arrow_1893660431le_alt,Z_3: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Z_3)),transi1687363644le_alt(R_2)))
     => ( ( X_2 != Z_3 )
       => ~ ! [Y_9: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_9)),R_2))
             => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_9),Z_3)),transi1687363644le_alt(R_2))) ) ) ) ).

tff(fact_861_rtranclE,axiom,
    ! [Aa: list_A114658244le_alt,Ba: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Ba)),transi1124010071le_alt(R_2)))
     => ( ( Aa != Ba )
       => ~ ! [Y_9: list_A114658244le_alt] :
              ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa),Y_9)),transi1124010071le_alt(R_2)))
             => ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Y_9),Ba)),R_2)) ) ) ) ).

tff(fact_862_rtranclE,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),transi1687363644le_alt(R_2)))
     => ( ( Aa != Ba )
       => ~ ! [Y_9: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Y_9)),transi1687363644le_alt(R_2)))
             => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_9),Ba)),R_2)) ) ) ) ).

tff(fact_863_split__list__first__propE,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ~ ! [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt] :
            ( ? [Zs: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
           => ( hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
             => ~ ! [Xa: arrow_1893660431le_alt] :
                    ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Xa),set_Ar1995755744le_alt(Ys)))
                   => ~ hBOOL(hAPP_A1748732503t_bool(Pa,Xa)) ) ) ) ) ).

tff(fact_864_split__list__last__propE,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ~ ! [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt,Zs: list_A114658244le_alt] :
            ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
           => ( hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
             => ~ ! [Xa: arrow_1893660431le_alt] :
                    ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Xa),set_Ar1995755744le_alt(Zs)))
                   => ~ hBOOL(hAPP_A1748732503t_bool(Pa,Xa)) ) ) ) ) ).

tff(fact_865_split__list__first,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ? [Ys: list_nat,Zs: list_nat] :
          ( ( Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) )
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Ys))) ) ) ).

tff(fact_866_split__list__first,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ? [Ys: list_A114658244le_alt,Zs: list_A114658244le_alt] :
          ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Ys))) ) ) ).

tff(fact_867_split__list__first,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ? [Ys: list_P662130680le_alt,Zs: list_P662130680le_alt] :
          ( ( Xs_1 = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Ys),hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Ys))) ) ) ).

tff(fact_868_split__list__first,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ? [Ys: list_A270647749e_indi,Zs: list_A270647749e_indi] :
          ( ( Xs_1 = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Ys),hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Zs)) )
          & ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Ys))) ) ) ).

tff(fact_869_split__list__first,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ? [Ys: list_bool,Zs: list_bool] :
          ( ( Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Ys))) ) ) ).

tff(fact_870_split__list__first,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ? [Ys: list_f1981087045t_bool,Zs: list_f1981087045t_bool] :
          ( ( Xs_1 = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Ys),hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Ys))) ) ) ).

tff(fact_871_split__list__first,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ? [Ys: list_f733367646t_bool,Zs: list_f733367646t_bool] :
          ( ( Xs_1 = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Ys),hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Ys))) ) ) ).

tff(fact_872_split__list__first,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ? [Ys: list_f1976315671t_bool,Zs: list_f1976315671t_bool] :
          ( ( Xs_1 = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Ys),hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Ys))) ) ) ).

tff(fact_873_split__list__first,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ? [Ys: list_P1419683592le_alt,Zs: list_P1419683592le_alt] :
          ( ( Xs_1 = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Ys),hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Ys))) ) ) ).

tff(fact_874_split__list__last,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ? [Ys: list_nat,Zs: list_nat] :
          ( ( Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) )
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Zs))) ) ) ).

tff(fact_875_split__list__last,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ? [Ys: list_A114658244le_alt,Zs: list_A114658244le_alt] :
          ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Zs))) ) ) ).

tff(fact_876_split__list__last,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ? [Ys: list_P662130680le_alt,Zs: list_P662130680le_alt] :
          ( ( Xs_1 = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Ys),hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Zs))) ) ) ).

tff(fact_877_split__list__last,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ? [Ys: list_A270647749e_indi,Zs: list_A270647749e_indi] :
          ( ( Xs_1 = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Ys),hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Zs)) )
          & ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Zs))) ) ) ).

tff(fact_878_split__list__last,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ? [Ys: list_bool,Zs: list_bool] :
          ( ( Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Zs))) ) ) ).

tff(fact_879_split__list__last,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ? [Ys: list_f1981087045t_bool,Zs: list_f1981087045t_bool] :
          ( ( Xs_1 = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Ys),hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Zs))) ) ) ).

tff(fact_880_split__list__last,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ? [Ys: list_f733367646t_bool,Zs: list_f733367646t_bool] :
          ( ( Xs_1 = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Ys),hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Zs))) ) ) ).

tff(fact_881_split__list__last,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ? [Ys: list_f1976315671t_bool,Zs: list_f1976315671t_bool] :
          ( ( Xs_1 = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Ys),hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Zs)) )
          & ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Zs))) ) ) ).

tff(fact_882_split__list__last,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ? [Ys: list_P1419683592le_alt,Zs: list_P1419683592le_alt] :
          ( ( Xs_1 = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Ys),hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Zs)) )
          & ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Zs))) ) ) ).

tff(fact_883_split__list,axiom,
    ! [X_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1)))
     => ? [Ys: list_nat,Zs: list_nat] : ( Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) ) ) ).

tff(fact_884_split__list,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1)))
     => ? [Ys: list_A114658244le_alt,Zs: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Zs)) ) ) ).

tff(fact_885_split__list,axiom,
    ! [X_2: produc587761367le_alt,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1)))
     => ? [Ys: list_P662130680le_alt,Zs: list_P662130680le_alt] : ( Xs_1 = hAPP_l922056661le_alt(hAPP_l581970330le_alt(append1796561362le_alt,Ys),hAPP_l922056661le_alt(hAPP_P1680517091le_alt(cons_P1273708151le_alt,X_2),Zs)) ) ) ).

tff(fact_886_split__list,axiom,
    ! [X_2: arrow_856714788e_indi,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1)))
     => ? [Ys: list_A270647749e_indi,Zs: list_A270647749e_indi] : ( Xs_1 = hAPP_l713773333e_indi(hAPP_l963769037e_indi(append139047327e_indi,Ys),hAPP_l713773333e_indi(hAPP_A1580343958e_indi(cons_A90150340e_indi,X_2),Zs)) ) ) ).

tff(fact_887_split__list,axiom,
    ! [X_2: bool,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1)))
     => ? [Ys: list_bool,Zs: list_bool] : ( Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) ) ) ).

tff(fact_888_split__list,axiom,
    ! [X_2: fun_fu2114379172t_bool,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1)))
     => ? [Ys: list_f1981087045t_bool,Zs: list_f1981087045t_bool] : ( Xs_1 = hAPP_l1936976149t_bool(hAPP_l2140505421t_bool(append34563871t_bool,Ys),hAPP_l1936976149t_bool(hAPP_f559469846t_bool(cons_f1814775108t_bool,X_2),Zs)) ) ) ).

tff(fact_889_split__list,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1)))
     => ? [Ys: list_f733367646t_bool,Zs: list_f733367646t_bool] : ( Xs_1 = hAPP_l1229506623t_bool(hAPP_l1290257408t_bool(append1496262254t_bool,Ys),hAPP_l1229506623t_bool(hAPP_f1754148237t_bool(cons_f1988942857t_bool,X_2),Zs)) ) ) ).

tff(fact_890_split__list,axiom,
    ! [X_2: fun_Ar274636406t_bool,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1)))
     => ? [Ys: list_f1976315671t_bool,Zs: list_f1976315671t_bool] : ( Xs_1 = hAPP_l179891349t_bool(hAPP_l352082555t_bool(append20579569t_bool,Ys),hAPP_l179891349t_bool(hAPP_f994423108t_bool(cons_f1976067606t_bool,X_2),Zs)) ) ) ).

tff(fact_891_split__list,axiom,
    ! [X_2: produc472769767le_alt,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1)))
     => ? [Ys: list_P1419683592le_alt,Zs: list_P1419683592le_alt] : ( Xs_1 = hAPP_l1424955733le_alt(hAPP_l1433766794le_alt(append200898658le_alt,Ys),hAPP_l1424955733le_alt(hAPP_P437856723le_alt(cons_P885197959le_alt,X_2),Zs)) ) ) ).

tff(fact_892_split__list__last__prop__iff,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
    <=> ? [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt,Zs: list_A114658244le_alt] :
          ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
          & ! [Xa: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Xa),set_Ar1995755744le_alt(Zs)))
             => ~ hBOOL(hAPP_A1748732503t_bool(Pa,Xa)) ) ) ) ).

tff(fact_893_split__list__first__prop__iff,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
    <=> ? [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt] :
          ( ? [Zs: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
          & ! [Xa: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Xa),set_Ar1995755744le_alt(Ys)))
             => ~ hBOOL(hAPP_A1748732503t_bool(Pa,Xa)) ) ) ) ).

tff(fact_894_list__update_Osimps_I2_J,axiom,
    ! [X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt,I_1: nat,V: arrow_1893660431le_alt] : ( hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(list_u1480779303le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)),I_1),V) = hAPP_n2007559481le_alt(nat_ca146784400le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,V),Xs_1),hAPP_f2082356689le_alt(hAPP_f162101723le_alt(cOMBB_138440792lt_nat,hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2)),hAPP_A890253665le_alt(hAPP_f752897057le_alt(cOMBC_100033222le_alt,list_u1480779303le_alt(Xs_1)),V))),I_1) ) ).

tff(fact_895_drop__Cons,axiom,
    ! [N_2: nat,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_n372949560le_alt(drop_A617527551le_alt,N_2),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_n2007559481le_alt(nat_ca146784400le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1),hAPP_l1210406190le_alt(hAPP_f1096875589le_alt(cOMBC_869637379le_alt,drop_A617527551le_alt),Xs_1)),N_2) ) ).

tff(fact_896_converse__rtranclE2,axiom,
    ! [Xa_1: list_A114658244le_alt,Xb: list_A114658244le_alt,Za: list_A114658244le_alt,Zb: list_A114658244le_alt,R_2: fun_Pr31738815t_bool] :
      ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xa_1),Xb)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Za),Zb))),transi434738282le_alt(R_2)))
     => ( ( hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xa_1),Xb) != hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Za),Zb) )
       => ~ ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt] :
              ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Xa_1),Xb)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6))),R_2))
             => ~ hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Za),Zb))),transi434738282le_alt(R_2))) ) ) ) ).

tff(fact_897_converse__rtranclE2,axiom,
    ! [Xa_1: arrow_1893660431le_alt,Xb: arrow_1893660431le_alt,Za: arrow_1893660431le_alt,Zb: arrow_1893660431le_alt,R_2: fun_Pr773225055t_bool] :
      ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Xa_1),Xb)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Za),Zb))),transi472504058le_alt(R_2)))
     => ( ( hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Xa_1),Xb) != hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Za),Zb) )
       => ~ ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Xa_1),Xb)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6))),R_2))
             => ~ hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Za),Zb))),transi472504058le_alt(R_2))) ) ) ) ).

tff(fact_898_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li495175091t_bool,Ax: list_A114658244le_alt,Ay: list_A114658244le_alt,Bx: list_A114658244le_alt,By: list_A114658244le_alt,R_2: fun_Pr31738815t_bool] :
      ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ax),Ay)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Bx),By))),transi434738282le_alt(R_2)))
     => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Bx),By))
       => ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt,Aa_1: list_A114658244le_alt,Ba_1: list_A114658244le_alt] :
              ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa_1),Ba_1))),R_2))
             => ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa_1),Ba_1)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Bx),By))),transi434738282le_alt(R_2)))
               => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Aa_1),Ba_1))
                 => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,A_7),B_6)) ) ) )
         => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_899_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Ar331856045t_bool,Ax: arrow_1893660431le_alt,Ay: arrow_1893660431le_alt,Bx: arrow_1893660431le_alt,By: arrow_1893660431le_alt,R_2: fun_Pr773225055t_bool] :
      ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ax),Ay)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Bx),By))),transi472504058le_alt(R_2)))
     => ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,Bx),By))
       => ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt,Aa_1: arrow_1893660431le_alt,Ba_1: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa_1),Ba_1))),R_2))
             => ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa_1),Ba_1)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Bx),By))),transi472504058le_alt(R_2)))
               => ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,Aa_1),Ba_1))
                 => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,A_7),B_6)) ) ) )
         => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_900_rtrancl__induct2,axiom,
    ! [Pa: fun_li495175091t_bool,Ax: list_A114658244le_alt,Ay: list_A114658244le_alt,Bx: list_A114658244le_alt,By: list_A114658244le_alt,R_2: fun_Pr31738815t_bool] :
      ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ax),Ay)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Bx),By))),transi434738282le_alt(R_2)))
     => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Ax),Ay))
       => ( ! [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt,Aa_1: list_A114658244le_alt,Ba_1: list_A114658244le_alt] :
              ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Ax),Ay)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6))),transi434738282le_alt(R_2)))
             => ( hBOOL(hAPP_f1525794055l_bool(hAPP_P1180049077l_bool(member74519274le_alt,hAPP_P740096983le_alt(hAPP_P1765681631le_alt(produc474284787le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6)),hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,Aa_1),Ba_1))),R_2))
               => ( hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,A_7),B_6))
                 => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Aa_1),Ba_1)) ) ) )
         => hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_901_rtrancl__induct2,axiom,
    ! [Pa: fun_Ar331856045t_bool,Ax: arrow_1893660431le_alt,Ay: arrow_1893660431le_alt,Bx: arrow_1893660431le_alt,By: arrow_1893660431le_alt,R_2: fun_Pr773225055t_bool] :
      ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ax),Ay)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Bx),By))),transi472504058le_alt(R_2)))
     => ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,Ax),Ay))
       => ( ! [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt,Aa_1: arrow_1893660431le_alt,Ba_1: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ax),Ay)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6))),transi472504058le_alt(R_2)))
             => ( hBOOL(hAPP_f1358512039l_bool(hAPP_P1862941685l_bool(member916027018le_alt,hAPP_P1322860167le_alt(hAPP_P1404837759le_alt(produc1036070419le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa_1),Ba_1))),R_2))
               => ( hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,A_7),B_6))
                 => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,Aa_1),Ba_1)) ) ) )
         => hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_902_take__Cons,axiom,
    ! [N_2: nat,X_2: arrow_1893660431le_alt,Xs_1: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_n372949560le_alt(take_A2032349095le_alt,N_2),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2),Xs_1)) = hAPP_n2007559481le_alt(nat_ca146784400le_alt(nil_Ar557011903le_alt,hAPP_f2082356689le_alt(hAPP_f162101723le_alt(cOMBB_138440792lt_nat,hAPP_A436723315le_alt(cons_A1647044463le_alt,X_2)),hAPP_l1210406190le_alt(hAPP_f1096875589le_alt(cOMBC_869637379le_alt,take_A2032349095le_alt),Xs_1))),N_2) ) ).

tff(fact_903_rtrancl_Osimps,axiom,
    ! [A1: list_A114658244le_alt,A2: list_A114658244le_alt,R_2: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A1),A2)),transi1124010071le_alt(R_2)))
    <=> ( ? [A_7: list_A114658244le_alt] :
            ( ( A1 = A_7 )
            & ( A2 = A_7 ) )
        | ? [A_7: list_A114658244le_alt,B_6: list_A114658244le_alt,C_5: list_A114658244le_alt] :
            ( ( A1 = A_7 )
            & ( A2 = C_5 )
            & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,A_7),B_6)),transi1124010071le_alt(R_2)))
            & hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,hAPP_l1580775710le_alt(hAPP_l660415097le_alt(produc1742925389le_alt,B_6),C_5)),R_2)) ) ) ) ).

tff(fact_904_rtrancl_Osimps,axiom,
    ! [A1: arrow_1893660431le_alt,A2: arrow_1893660431le_alt,R_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A1),A2)),transi1687363644le_alt(R_2)))
    <=> ( ? [A_7: arrow_1893660431le_alt] :
            ( ( A1 = A_7 )
            & ( A2 = A_7 ) )
        | ? [A_7: arrow_1893660431le_alt,B_6: arrow_1893660431le_alt,C_5: arrow_1893660431le_alt] :
            ( ( A1 = A_7 )
            & ( A2 = C_5 )
            & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_7),B_6)),transi1687363644le_alt(R_2)))
            & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,B_6),C_5)),R_2)) ) ) ) ).

tff(fact_905_listrel__subset__rtrancl__listrel1,axiom,
    ! [R_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,hAPP_f369701637t_bool(listre1191473383le_alt,R_2)),transi1124010071le_alt(hAPP_f369701637t_bool(listre1334820888le_alt,R_2)))) ).

tff(fact_906_split__list__first__prop,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ? [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt] :
          ( ? [Zs: list_A114658244le_alt] : ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
          & ! [Xa: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Xa),set_Ar1995755744le_alt(Ys)))
             => ~ hBOOL(hAPP_A1748732503t_bool(Pa,Xa)) ) ) ) ).

tff(fact_907_split__list__last__prop,axiom,
    ! [Pa: fun_Ar17477381t_bool,Xs_1: list_A114658244le_alt] :
      ( ? [X_1: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_1),set_Ar1995755744le_alt(Xs_1)))
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1)) )
     => ? [Ys: list_A114658244le_alt,X_1: arrow_1893660431le_alt,Zs: list_A114658244le_alt] :
          ( ( Xs_1 = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,Ys),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X_1),Zs)) )
          & hBOOL(hAPP_A1748732503t_bool(Pa,X_1))
          & ! [Xa: arrow_1893660431le_alt] :
              ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Xa),set_Ar1995755744le_alt(Zs)))
             => ~ hBOOL(hAPP_A1748732503t_bool(Pa,Xa)) ) ) ) ).

tff(fact_908_order__refl,axiom,
    ! [X_10: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),X_10)) ).

tff(fact_909_subsetD,axiom,
    ! [Ca: nat,A_1: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_1)) ) ) ).

tff(fact_910_subsetD,axiom,
    ! [Ca: arrow_1893660431le_alt,A_1: fun_Ar17477381t_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Ca),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,Ca),B_1)) ) ) ).

tff(fact_911_subsetD,axiom,
    ! [Ca: produc587761367le_alt,A_1: fun_Pr486337689t_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Ca),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,Ca),B_1)) ) ) ).

tff(fact_912_subsetD,axiom,
    ! [Ca: arrow_856714788e_indi,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A_1),B_1))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Ca),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Ca),B_1)) ) ) ).

tff(fact_913_subsetD,axiom,
    ! [Ca: bool,A_1: fun_bool_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B_1)) ) ) ).

tff(fact_914_subsetD,axiom,
    ! [Ca: fun_fu2114379172t_bool,A_1: fun_fu2098777574l_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Ca),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Ca),B_1)) ) ) ).

tff(fact_915_subsetD,axiom,
    ! [Ca: fun_Pr2067565481t_bool,A_1: fun_fu638310559l_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Ca),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Ca),B_1)) ) ) ).

tff(fact_916_subsetD,axiom,
    ! [Ca: fun_Ar274636406t_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Ca),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Ca),B_1)) ) ) ).

tff(fact_917_subsetD,axiom,
    ! [Ca: produc472769767le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Ca),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Ca),B_1)) ) ) ).

tff(fact_918_listrel__mono,axiom,
    ! [R_2: fun_Pr2067565481t_bool,S_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,R_2),S_2))
     => hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,hAPP_f369701637t_bool(listre1191473383le_alt,R_2)),hAPP_f369701637t_bool(listre1191473383le_alt,S_2))) ) ).

tff(fact_919_listrel1__mono,axiom,
    ! [R_2: fun_Pr2067565481t_bool,S_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,R_2),S_2))
     => hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,hAPP_f369701637t_bool(listre1334820888le_alt,R_2)),hAPP_f369701637t_bool(listre1334820888le_alt,S_2))) ) ).

tff(fact_920_Pi__anti__mono,axiom,
    ! [B_1: fun_Pr1780397033l_bool,A_6: fun_Pr2067565481t_bool,A_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A_6),A_1))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,pi_Pro1238944957t_bool(A_1,B_1)),pi_Pro1238944957t_bool(A_6,B_1))) ) ).

tff(fact_921_Pi__anti__mono,axiom,
    ! [B_1: fun_Ar1474557608l_bool,A_6: fun_Ar1809396326i_bool,A_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A_6),A_1))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,pi_Arr959578316t_bool(A_1,B_1)),pi_Arr959578316t_bool(A_6,B_1))) ) ).

tff(fact_922_Pi__anti__mono,axiom,
    ! [B_1: fun_fu1863781882l_bool,A_6: fun_fu3835832l_bool,A_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A_6),A_1))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,pi_fun1746584570t_bool(A_1,B_1)),pi_fun1746584570t_bool(A_6,B_1))) ) ).

tff(fact_923_pred__subset__eq,axiom,
    ! [R_1: fun_nat_bool,S_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) ) ).

tff(fact_924_pred__subset__eq,axiom,
    ! [R_1: fun_Ar17477381t_bool,S_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,hAPP_f1592536333t_bool(hAPP_f1090944335t_bool(cOMBC_1310341090l_bool,member1502664802le_alt),R_1)),hAPP_f1592536333t_bool(hAPP_f1090944335t_bool(cOMBC_1310341090l_bool,member1502664802le_alt),S_1)))
    <=> hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,R_1),S_1)) ) ).

tff(fact_925_pred__subset__eq,axiom,
    ! [R_1: fun_Pr486337689t_bool,S_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,hAPP_f2146417685t_bool(hAPP_f1616253255t_bool(cOMBC_1249985698l_bool,member1401409220le_alt),R_1)),hAPP_f2146417685t_bool(hAPP_f1616253255t_bool(cOMBC_1249985698l_bool,member1401409220le_alt),S_1)))
    <=> hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,R_1),S_1)) ) ).

tff(fact_926_pred__subset__eq,axiom,
    ! [R_1: fun_Ar1809396326i_bool,S_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_f1612707285i_bool(hAPP_f1615874669i_bool(cOMBC_438428898l_bool,member1479139729e_indi),R_1)),hAPP_f1612707285i_bool(hAPP_f1615874669i_bool(cOMBC_438428898l_bool,member1479139729e_indi),S_1)))
    <=> hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,R_1),S_1)) ) ).

tff(fact_927_pred__subset__eq,axiom,
    ! [R_1: fun_bool_bool,S_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1)))
    <=> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)) ) ).

tff(fact_928_pred__subset__eq,axiom,
    ! [R_1: fun_fu2098777574l_bool,S_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_f1181604821l_bool(hAPP_f1169241965l_bool(cOMBC_1209358050l_bool,member173038353t_bool),R_1)),hAPP_f1181604821l_bool(hAPP_f1169241965l_bool(cOMBC_1209358050l_bool,member173038353t_bool),S_1)))
    <=> hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,R_1),S_1)) ) ).

tff(fact_929_pred__subset__eq,axiom,
    ! [R_1: fun_fu638310559l_bool,S_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_f1060563265l_bool(hAPP_f1776355587l_bool(cOMBC_2133093654l_bool,member1069471740t_bool),R_1)),hAPP_f1060563265l_bool(hAPP_f1776355587l_bool(cOMBC_2133093654l_bool,member1069471740t_bool),S_1)))
    <=> hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,R_1),S_1)) ) ).

tff(fact_930_pred__subset__eq,axiom,
    ! [R_1: fun_fu3835832l_bool,S_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_f819682389l_bool(hAPP_f1760776521l_bool(cOMBC_514203746l_bool,member933336803t_bool),R_1)),hAPP_f819682389l_bool(hAPP_f1760776521l_bool(cOMBC_514203746l_bool,member933336803t_bool),S_1)))
    <=> hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,R_1),S_1)) ) ).

tff(fact_931_pred__subset__eq,axiom,
    ! [R_1: fun_Pr2067565481t_bool,S_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_f1356305429t_bool(hAPP_f1033183015t_bool(cOMBC_593569186l_bool,member1333168212le_alt),R_1)),hAPP_f1356305429t_bool(hAPP_f1033183015t_bool(cOMBC_593569186l_bool,member1333168212le_alt),S_1)))
    <=> hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,R_1),S_1)) ) ).

tff(fact_932_linorder__le__cases,axiom,
    ! [X_9: nat,Y_8: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_8),X_9)) ) ).

tff(fact_933_xt1_I6_J,axiom,
    ! [Z_2: nat,Y_7: nat,X_8: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_2),Y_7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_2),X_8)) ) ) ).

tff(fact_934_xt1_I5_J,axiom,
    ! [Y_6: nat,X_7: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_7))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6))
       => ( X_7 = Y_6 ) ) ) ).

tff(fact_935_order__trans,axiom,
    ! [Z_1: nat,X_6: nat,Y_5: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),Z_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Z_1)) ) ) ).

tff(fact_936_order__antisym,axiom,
    ! [X_5: nat,Y_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_5),Y_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5))
       => ( X_5 = Y_4 ) ) ) ).

tff(fact_937_xt1_I4_J,axiom,
    ! [C_4: nat,B_5: nat,A_5: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),A_5))
     => ( ( B_5 = C_4 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_4),A_5)) ) ) ).

tff(fact_938_ord__le__eq__trans,axiom,
    ! [C_3: nat,A_4: nat,B_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),B_4))
     => ( ( B_4 = C_3 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),C_3)) ) ) ).

tff(fact_939_set__mp,axiom,
    ! [X_2: nat,A_1: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1)) ) ) ).

tff(fact_940_set__mp,axiom,
    ! [X_2: arrow_1893660431le_alt,A_1: fun_Ar17477381t_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),B_1)) ) ) ).

tff(fact_941_set__mp,axiom,
    ! [X_2: produc587761367le_alt,A_1: fun_Pr486337689t_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),B_1)) ) ) ).

tff(fact_942_set__mp,axiom,
    ! [X_2: arrow_856714788e_indi,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A_1),B_1))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),B_1)) ) ) ).

tff(fact_943_set__mp,axiom,
    ! [X_2: bool,A_1: fun_bool_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B_1)) ) ) ).

tff(fact_944_set__mp,axiom,
    ! [X_2: fun_fu2114379172t_bool,A_1: fun_fu2098777574l_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),B_1)) ) ) ).

tff(fact_945_set__mp,axiom,
    ! [X_2: fun_Pr2067565481t_bool,A_1: fun_fu638310559l_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),B_1)) ) ) ).

tff(fact_946_set__mp,axiom,
    ! [X_2: fun_Ar274636406t_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),B_1)) ) ) ).

tff(fact_947_set__mp,axiom,
    ! [X_2: produc472769767le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),B_1)) ) ) ).

tff(fact_948_set__rev__mp,axiom,
    ! [B_1: fun_nat_bool,X_2: nat,A_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1)) ) ) ).

tff(fact_949_set__rev__mp,axiom,
    ! [B_1: fun_Ar17477381t_bool,X_2: arrow_1893660431le_alt,A_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,A_1),B_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),B_1)) ) ) ).

tff(fact_950_set__rev__mp,axiom,
    ! [B_1: fun_Pr486337689t_bool,X_2: produc587761367le_alt,A_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,A_1),B_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),B_1)) ) ) ).

tff(fact_951_set__rev__mp,axiom,
    ! [B_1: fun_Ar1809396326i_bool,X_2: arrow_856714788e_indi,A_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A_1),B_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),B_1)) ) ) ).

tff(fact_952_set__rev__mp,axiom,
    ! [B_1: fun_bool_bool,X_2: bool,A_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B_1)) ) ) ).

tff(fact_953_set__rev__mp,axiom,
    ! [B_1: fun_fu2098777574l_bool,X_2: fun_fu2114379172t_bool,A_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A_1),B_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),B_1)) ) ) ).

tff(fact_954_set__rev__mp,axiom,
    ! [B_1: fun_fu638310559l_bool,X_2: fun_Pr2067565481t_bool,A_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A_1),B_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),B_1)) ) ) ).

tff(fact_955_set__rev__mp,axiom,
    ! [B_1: fun_fu3835832l_bool,X_2: fun_Ar274636406t_bool,A_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A_1),B_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),B_1)) ) ) ).

tff(fact_956_set__rev__mp,axiom,
    ! [B_1: fun_Pr2067565481t_bool,X_2: produc472769767le_alt,A_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A_1),B_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),B_1)) ) ) ).

tff(fact_957_xt1_I3_J,axiom,
    ! [C_2: nat,A_3: nat,B_3: nat] :
      ( ( A_3 = B_3 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_2),B_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_2),A_3)) ) ) ).

tff(fact_958_ord__eq__le__trans,axiom,
    ! [C_1: nat,A_2: nat,B_2: nat] :
      ( ( A_2 = B_2 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),C_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),C_1)) ) ) ).

tff(fact_959_order__antisym__conv,axiom,
    ! [Y_2: nat,X_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_960_in__mono,axiom,
    ! [X_2: nat,A_1: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1)) ) ) ).

tff(fact_961_in__mono,axiom,
    ! [X_2: arrow_1893660431le_alt,A_1: fun_Ar17477381t_bool,B_1: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),A_1))
       => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),B_1)) ) ) ).

tff(fact_962_in__mono,axiom,
    ! [X_2: produc587761367le_alt,A_1: fun_Pr486337689t_bool,B_1: fun_Pr486337689t_bool] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_f193216531l_bool(ord_le907370723t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),A_1))
       => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),B_1)) ) ) ).

tff(fact_963_in__mono,axiom,
    ! [X_2: arrow_856714788e_indi,A_1: fun_Ar1809396326i_bool,B_1: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A_1),B_1))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A_1))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),B_1)) ) ) ).

tff(fact_964_in__mono,axiom,
    ! [X_2: bool,A_1: fun_bool_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B_1)) ) ) ).

tff(fact_965_in__mono,axiom,
    ! [X_2: fun_fu2114379172t_bool,A_1: fun_fu2098777574l_bool,B_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A_1))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),B_1)) ) ) ).

tff(fact_966_in__mono,axiom,
    ! [X_2: fun_Pr2067565481t_bool,A_1: fun_fu638310559l_bool,B_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A_1))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),B_1)) ) ) ).

tff(fact_967_in__mono,axiom,
    ! [X_2: fun_Ar274636406t_bool,A_1: fun_fu3835832l_bool,B_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A_1),B_1))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A_1))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),B_1)) ) ) ).

tff(fact_968_in__mono,axiom,
    ! [X_2: produc472769767le_alt,A_1: fun_Pr2067565481t_bool,B_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A_1),B_1))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A_1))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),B_1)) ) ) ).

tff(fact_969_order__eq__refl,axiom,
    ! [X_4: nat,Y_3: nat] :
      ( ( X_4 = Y_3 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)) ) ).

tff(fact_970_order__eq__iff,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).

tff(fact_971_linorder__linear,axiom,
    ! [X_3: nat,Y_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_3)) ) ).

tff(fact_972_take__Nil,axiom,
    ! [N_3: nat] : ( hAPP_l84111627le_alt(hAPP_n372949560le_alt(take_A2032349095le_alt,N_3),nil_Ar557011903le_alt) = nil_Ar557011903le_alt ) ).

tff(fact_973_in__set__takeD,axiom,
    ! [X_2: nat,N_2: nat,Xs_1: list_nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_2),Xs_1))))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) ) ).

tff(fact_974_in__set__takeD,axiom,
    ! [X_2: arrow_1893660431le_alt,N_2: nat,Xs_1: list_A114658244le_alt] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_n372949560le_alt(take_A2032349095le_alt,N_2),Xs_1))))
     => hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X_2),set_Ar1995755744le_alt(Xs_1))) ) ).

tff(fact_975_in__set__takeD,axiom,
    ! [X_2: produc587761367le_alt,N_2: nat,Xs_1: list_P662130680le_alt] :
      ( hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(hAPP_l922056661le_alt(hAPP_n648772104le_alt(take_P961419327le_alt,N_2),Xs_1))))
     => hBOOL(hAPP_f610613473l_bool(hAPP_P489291369l_bool(member1401409220le_alt,X_2),set_Pr1785012934le_alt(Xs_1))) ) ).

tff(fact_976_in__set__takeD,axiom,
    ! [X_2: arrow_856714788e_indi,N_2: nat,Xs_1: list_A270647749e_indi] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(hAPP_l713773333e_indi(hAPP_n914286664e_indi(take_A1953651596e_indi,N_2),Xs_1))))
     => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),set_Ar205654163e_indi(Xs_1))) ) ).

tff(fact_977_in__set__takeD,axiom,
    ! [X_2: bool,N_2: nat,Xs_1: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) ) ).

tff(fact_978_in__set__takeD,axiom,
    ! [X_2: fun_fu2114379172t_bool,N_2: nat,Xs_1: list_f1981087045t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(hAPP_l1936976149t_bool(hAPP_n679397960t_bool(take_f1080892172t_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),set_fu2135320083t_bool(Xs_1))) ) ).

tff(fact_979_in__set__takeD,axiom,
    ! [X_2: fun_Pr2067565481t_bool,N_2: nat,Xs_1: list_f733367646t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(hAPP_l1229506623t_bool(hAPP_n435915628t_bool(take_f362945601t_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),set_fu1957445242t_bool(Xs_1))) ) ).

tff(fact_980_in__set__takeD,axiom,
    ! [X_2: fun_Ar274636406t_bool,N_2: nat,Xs_1: list_f1976315671t_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(hAPP_l179891349t_bool(hAPP_n1109524424t_bool(take_f1842263006t_bool,N_2),Xs_1))))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),set_fu2037886949t_bool(Xs_1))) ) ).

tff(fact_981_in__set__takeD,axiom,
    ! [X_2: produc472769767le_alt,N_2: nat,Xs_1: list_P1419683592le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(hAPP_l1424955733le_alt(hAPP_n1575317256le_alt(take_P1172918863le_alt,N_2),Xs_1))))
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),set_Pr496668502le_alt(Xs_1))) ) ).

tff(fact_982_distinct__take,axiom,
    ! [I_3: nat,Xs: list_A114658244le_alt] :
      ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,Xs))
     => hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_n372949560le_alt(take_A2032349095le_alt,I_3),Xs))) ) ).

tff(fact_983_top__greatest,axiom,
    ! [Aa: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)) ).

tff(fact_984_top__greatest,axiom,
    ! [Aa: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),top_to1138392227t_bool)) ).

tff(fact_985_top__greatest,axiom,
    ! [Aa: fun_fu3835832l_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),top_to553140914l_bool)) ).

tff(fact_986_top__greatest,axiom,
    ! [Aa: fun_fu638310559l_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),top_to1312956197l_bool)) ).

tff(fact_987_top__greatest,axiom,
    ! [Aa: fun_fu2098777574l_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),top_to827110112l_bool)) ).

tff(fact_988_top__greatest,axiom,
    ! [Aa: fun_Ar17477381t_bool] : hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,Aa),top_to814956427t_bool)) ).

tff(fact_989_top__greatest,axiom,
    ! [Aa: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),top_to788185952i_bool)) ).

tff(fact_990_top__unique,axiom,
    ! [Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
    <=> ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ) ).

tff(fact_991_top__unique,axiom,
    ! [Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,top_to1138392227t_bool),Aa))
    <=> ( Aa = top_to1138392227t_bool ) ) ).

tff(fact_992_top__unique,axiom,
    ! [Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,top_to553140914l_bool),Aa))
    <=> ( Aa = top_to553140914l_bool ) ) ).

tff(fact_993_top__unique,axiom,
    ! [Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,top_to1312956197l_bool),Aa))
    <=> ( Aa = top_to1312956197l_bool ) ) ).

tff(fact_994_top__unique,axiom,
    ! [Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,top_to827110112l_bool),Aa))
    <=> ( Aa = top_to827110112l_bool ) ) ).

tff(fact_995_top__unique,axiom,
    ! [Aa: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,top_to814956427t_bool),Aa))
    <=> ( Aa = top_to814956427t_bool ) ) ).

tff(fact_996_top__unique,axiom,
    ! [Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,top_to788185952i_bool),Aa))
    <=> ( Aa = top_to788185952i_bool ) ) ).

tff(fact_997_top__le,axiom,
    ! [Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,top_to1138392227t_bool),Aa))
     => ( Aa = top_to1138392227t_bool ) ) ).

tff(fact_998_top__le,axiom,
    ! [Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,top_to553140914l_bool),Aa))
     => ( Aa = top_to553140914l_bool ) ) ).

tff(fact_999_top__le,axiom,
    ! [Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,top_to1312956197l_bool),Aa))
     => ( Aa = top_to1312956197l_bool ) ) ).

tff(fact_1000_top__le,axiom,
    ! [Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,top_to827110112l_bool),Aa))
     => ( Aa = top_to827110112l_bool ) ) ).

tff(fact_1001_top__le,axiom,
    ! [Aa: fun_Ar17477381t_bool] :
      ( hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,top_to814956427t_bool),Aa))
     => ( Aa = top_to814956427t_bool ) ) ).

tff(fact_1002_top__le,axiom,
    ! [Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,top_to788185952i_bool),Aa))
     => ( Aa = top_to788185952i_bool ) ) ).

tff(fact_1003_termination__basic__simps_I5_J,axiom,
    ! [X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ).

tff(fact_1004_lessI,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))) ).

tff(fact_1005_Suc__mono,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1006_less__eq__Suc__le__raw,axiom,
    ! [X_1: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)) ) ).

tff(fact_1007_n__not__Suc__n,axiom,
    ! [N: nat] : ( N != hAPP_nat_nat(suc,N) ) ).

tff(fact_1008_Suc__n__not__n,axiom,
    ! [N: nat] : ( hAPP_nat_nat(suc,N) != N ) ).

tff(fact_1009_nat_Oinject,axiom,
    ! [Nat_5: nat,Nat_4: nat] :
      ( ( hAPP_nat_nat(suc,Nat_5) = hAPP_nat_nat(suc,Nat_4) )
    <=> ( Nat_5 = Nat_4 ) ) ).

tff(fact_1010_Suc__inject,axiom,
    ! [X: nat,Y: nat] :
      ( ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) )
     => ( X = Y ) ) ).

tff(fact_1011_less__not__refl,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ).

tff(fact_1012_nat__neq__iff,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ( M_2 != N_2 )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)) ) ) ).

tff(fact_1013_linorder__neqE__nat,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).

tff(fact_1014_less__irrefl__nat,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ).

tff(fact_1015_less__not__refl2,axiom,
    ! [N: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
     => ( M != N ) ) ).

tff(fact_1016_less__not__refl3,axiom,
    ! [S: nat,T: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => ( S != T ) ) ).

tff(fact_1017_nat__less__cases,axiom,
    ! [Pa: fun_nat_fun_nat_bool,M_2: nat,N_2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2)) )
     => ( ( ( M_2 = N_2 )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2)) ) ) ) ).

tff(fact_1018_le__refl,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)) ).

tff(fact_1019_nat__le__linear,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ).

tff(fact_1020_eq__imp__le,axiom,
    ! [M: nat,N: nat] :
      ( ( M = N )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).

tff(fact_1021_le__trans,axiom,
    ! [K_2: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) ) ) ).

tff(fact_1022_le__antisym,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
       => ( M = N ) ) ) ).

tff(fact_1023_Suc__less__SucD,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).

tff(fact_1024_Suc__lessD,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).

tff(fact_1025_less__SucE,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
       => ( M = N ) ) ) ).

tff(fact_1026_less__trans__Suc,axiom,
    ! [K_2: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2)) ) ) ).

tff(fact_1027_Suc__lessI,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ( ( hAPP_nat_nat(suc,M) != N )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) ) ) ).

tff(fact_1028_less__SucI,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1029_less__antisym,axiom,
    ! [N: nat,M: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M)))
       => ( M = N ) ) ) ).

tff(fact_1030_not__less__less__Suc__eq,axiom,
    ! [N_2: nat,M_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2)))
      <=> ( N_2 = M_2 ) ) ) ).

tff(fact_1031_Suc__less__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).

tff(fact_1032_less__Suc__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
        | ( M_2 = N_2 ) ) ) ).

tff(fact_1033_not__less__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2))) ) ).

tff(fact_1034_Suc__n__not__le__n,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)) ).

tff(fact_1035_not__less__eq__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_2)) ) ).

tff(fact_1036_le__Suc__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
        | ( M_2 = hAPP_nat_nat(suc,N_2) ) ) ) ).

tff(fact_1037_Suc__le__mono,axiom,
    ! [N_2: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),hAPP_nat_nat(suc,M_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) ) ).

tff(fact_1038_le__SucI,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1039_le__SucE,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
       => ( M = hAPP_nat_nat(suc,N) ) ) ) ).

tff(fact_1040_Suc__leD,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).

tff(fact_1041_less__or__eq__imp__le,axiom,
    ! [M: nat,N: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
        | ( M = N ) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).

tff(fact_1042_le__neq__implies__less,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => ( ( M != N )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ) ).

tff(fact_1043_less__imp__le__nat,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).

tff(fact_1044_le__eq__less__or__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
        | ( M_2 = N_2 ) ) ) ).

tff(fact_1045_nat__less__le,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
        & ( M_2 != N_2 ) ) ) ).

tff(fact_1046_less__eq__Suc__le,axiom,
    ! [N_2: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_2)) ) ).

tff(fact_1047_less__Suc__eq__le,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).

tff(fact_1048_Suc__le__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).

tff(fact_1049_le__imp__less__Suc,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1050_Suc__leI,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) ) ).

tff(fact_1051_le__less__Suc__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2)))
      <=> ( N_2 = M_2 ) ) ) ).

tff(fact_1052_Suc__le__lessD,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).

tff(fact_1053_inc__induct,axiom,
    ! [Pa: fun_nat_bool,I_1: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2))
     => ( hBOOL(hAPP_nat_bool(Pa,J_2))
       => ( ! [I: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I)))
               => hBOOL(hAPP_nat_bool(Pa,I)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I_1)) ) ) ) ).

tff(fact_1054_less__eq__nat_Osimps_I2_J,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2))
    <=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_2)),N_2)) ) ).

tff(fact_1055_less__mono__imp__le__mono,axiom,
    ! [I_1: nat,J_2: nat,F: fun_nat_nat] :
      ( ! [I: nat,J_1: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J_1))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2))) ) ) ).

tff(fact_1056_Suc__le__D,axiom,
    ! [N: nat,M_3: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3))
     => ? [M_1: nat] : ( M_3 = hAPP_nat_nat(suc,M_1) ) ) ).

tff(fact_1057_lessE,axiom,
    ! [I_2: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
     => ( ( K_2 != hAPP_nat_nat(suc,I_2) )
       => ~ ! [J_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
             => ( K_2 != hAPP_nat_nat(suc,J_1) ) ) ) ) ).

tff(fact_1058_Suc__lessE,axiom,
    ! [I_2: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2))
     => ~ ! [J_1: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
           => ( K_2 != hAPP_nat_nat(suc,J_1) ) ) ) ).

tff(fact_1059_termination__basic__simps_I1_J,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) ) ).

tff(fact_1060_termination__basic__simps_I2_J,axiom,
    ! [Y: nat,X: nat,Z: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) ) ).

tff(fact_1061_add__lessD1,axiom,
    ! [I_2: nat,J: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),J)),K_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) ) ).

tff(fact_1062_less__add__eq__less,axiom,
    ! [M: nat,N: nat,K_2: nat,L: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L))
     => ( ( hAPP_nat_nat(plus_plus_nat(M),L) = hAPP_nat_nat(plus_plus_nat(K_2),N) )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ) ).

tff(fact_1063_add__less__mono,axiom,
    ! [K_2: nat,L: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),L))) ) ) ).

tff(fact_1064_add__less__mono1,axiom,
    ! [K_2: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),K_2))) ) ).

tff(fact_1065_trans__less__add2,axiom,
    ! [M: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(plus_plus_nat(M),J))) ) ).

tff(fact_1066_trans__less__add1,axiom,
    ! [M: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(plus_plus_nat(J),M))) ) ).

tff(fact_1067_nat__add__left__cancel__less,axiom,
    ! [K: nat,M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K),M_2)),hAPP_nat_nat(plus_plus_nat(K),N_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).

tff(fact_1068_not__add__less2,axiom,
    ! [J: nat,I_2: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J),I_2)),I_2)) ).

tff(fact_1069_not__add__less1,axiom,
    ! [I_2: nat,J: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),J)),I_2)) ).

tff(fact_1070_termination__basic__simps_I3_J,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) ) ).

tff(fact_1071_termination__basic__simps_I4_J,axiom,
    ! [Y: nat,X: nat,Z: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))) ) ).

tff(fact_1072_le__add2,axiom,
    ! [N: nat,M: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(M),N))) ).

tff(fact_1073_le__add1,axiom,
    ! [N: nat,M: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(N),M))) ).

tff(fact_1074_le__iff__add,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
    <=> ? [K_1: nat] : ( N_2 = hAPP_nat_nat(plus_plus_nat(M_2),K_1) ) ) ).

tff(fact_1075_nat__add__left__cancel__le,axiom,
    ! [K: nat,M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K),M_2)),hAPP_nat_nat(plus_plus_nat(K),N_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).

tff(fact_1076_trans__le__add1,axiom,
    ! [M: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(plus_plus_nat(J),M))) ) ).

tff(fact_1077_trans__le__add2,axiom,
    ! [M: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(plus_plus_nat(M),J))) ) ).

tff(fact_1078_add__le__mono1,axiom,
    ! [K_2: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),K_2))) ) ).

tff(fact_1079_add__le__mono,axiom,
    ! [K_2: nat,L: nat,I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),L))) ) ) ).

tff(fact_1080_add__leD2,axiom,
    ! [M: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ).

tff(fact_1081_add__leD1,axiom,
    ! [M: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).

tff(fact_1082_add__leE,axiom,
    ! [M: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_2)),N))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ) ).

tff(fact_1083_add__Suc__right,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)) ) ).

tff(fact_1084_add__Suc,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)) ) ).

tff(fact_1085_add__Suc__shift,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) ) ).

tff(fact_1086_min__Suc__Suc,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N)) ) ).

tff(fact_1087_nat__add__right__cancel,axiom,
    ! [M_2: nat,K: nat,N_2: nat] :
      ( ( hAPP_nat_nat(plus_plus_nat(M_2),K) = hAPP_nat_nat(plus_plus_nat(N_2),K) )
    <=> ( M_2 = N_2 ) ) ).

tff(fact_1088_nat__add__left__cancel,axiom,
    ! [K: nat,M_2: nat,N_2: nat] :
      ( ( hAPP_nat_nat(plus_plus_nat(K),M_2) = hAPP_nat_nat(plus_plus_nat(K),N_2) )
    <=> ( M_2 = N_2 ) ) ).

tff(fact_1089_nat__add__assoc,axiom,
    ! [M: nat,N: nat,K_2: nat] : ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),K_2) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N),K_2)) ) ).

tff(fact_1090_nat__add__left__commute,axiom,
    ! [X: nat,Y: nat,Z: nat] : ( hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z)) ) ).

tff(fact_1091_nat__add__commute,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(plus_plus_nat(M),N) = hAPP_nat_nat(plus_plus_nat(N),M) ) ).

tff(fact_1092_less__iff__Suc__add,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
    <=> ? [K_1: nat] : ( N_2 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_2),K_1)) ) ) ).

tff(fact_1093_less__add__Suc2,axiom,
    ! [I_2: nat,M: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I_2)))) ).

tff(fact_1094_less__add__Suc1,axiom,
    ! [I_2: nat,M: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I_2),M)))) ).

tff(fact_1095_mono__nat__linear__lb,axiom,
    ! [M_2: nat,K: nat,F: fun_nat_nat] :
      ( ! [M_1: nat,N_1: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_1)),hAPP_nat_nat(F,N_1))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_2)),K)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_2),K)))) ) ).

tff(fact_1096_less__imp__Suc__add,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ? [K_1: nat] : ( N = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),K_1)) ) ) ).

tff(fact_1097_weak__decr__stable,axiom,
    ! [F: fun_nat_nat] :
      ( ! [I: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I))),hAPP_nat_nat(F,I)))
     => ? [I: nat] :
        ! [K_1: nat] : ( hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(I),K_1)) = hAPP_nat_nat(F,I) ) ) ).

tff(fact_1098_less__zeroE,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).

tff(fact_1099_le0,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ).

tff(fact_1100_zero__less__Suc,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))) ).

tff(fact_1101_nat__diff__split,axiom,
    ! [Pa: fun_nat_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(Aa),Ba)))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
         => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) )
        & ! [D: nat] :
            ( ( Aa = hAPP_nat_nat(plus_plus_nat(Ba),D) )
           => hBOOL(hAPP_nat_bool(Pa,D)) ) ) ) ).

tff(fact_1102_nat__diff__split__asm,axiom,
    ! [Pa: fun_nat_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(Aa),Ba)))
    <=> ~ ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
            & ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) )
          | ? [D: nat] :
              ( ( Aa = hAPP_nat_nat(plus_plus_nat(Ba),D) )
              & ~ hBOOL(hAPP_nat_bool(Pa,D)) ) ) ) ).

tff(fact_1103_add__eq__self__zero,axiom,
    ! [M: nat,N: nat] :
      ( ( hAPP_nat_nat(plus_plus_nat(M),N) = M )
     => ( N = zero_zero_nat ) ) ).

tff(fact_1104_min__diff,axiom,
    ! [M: nat,I_2: nat,N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(minus_minus_nat(M),I_2)),hAPP_nat_nat(minus_minus_nat(N),I_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N)),I_2) ) ).

tff(fact_1105_diff__cancel2,axiom,
    ! [M: nat,K_2: nat,N: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K_2)),hAPP_nat_nat(plus_plus_nat(N),K_2)) = hAPP_nat_nat(minus_minus_nat(M),N) ) ).

tff(fact_1106_diff__cancel,axiom,
    ! [K_2: nat,M: nat,N: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K_2),M)),hAPP_nat_nat(plus_plus_nat(K_2),N)) = hAPP_nat_nat(minus_minus_nat(M),N) ) ).

tff(fact_1107_diff__diff__left,axiom,
    ! [I_2: nat,J: nat,K_2: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_2),J)),K_2) = hAPP_nat_nat(minus_minus_nat(I_2),hAPP_nat_nat(plus_plus_nat(J),K_2)) ) ).

tff(fact_1108_diff__add__inverse,axiom,
    ! [N: nat,M: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),N) = M ) ).

tff(fact_1109_diff__add__inverse2,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),N) = M ) ).

tff(fact_1110_add__is__0,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ( hAPP_nat_nat(plus_plus_nat(M_2),N_2) = zero_zero_nat )
    <=> ( ( M_2 = zero_zero_nat )
        & ( N_2 = zero_zero_nat ) ) ) ).

tff(fact_1111_diff__add__0,axiom,
    ! [N: nat,M: nat] : ( hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(plus_plus_nat(N),M)) = zero_zero_nat ) ).

tff(fact_1112_Nat_Oadd__0__right,axiom,
    ! [M: nat] : ( hAPP_nat_nat(plus_plus_nat(M),zero_zero_nat) = M ) ).

tff(fact_1113_min__0R,axiom,
    ! [N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N),zero_zero_nat) = zero_zero_nat ) ).

tff(fact_1114_plus__nat_Oadd__0,axiom,
    ! [N: nat] : ( hAPP_nat_nat(plus_plus_nat(zero_zero_nat),N) = N ) ).

tff(fact_1115_min__0L,axiom,
    ! [N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),N) = zero_zero_nat ) ).

tff(fact_1116_Suc__pred,axiom,
    ! [N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ( hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(suc,zero_zero_nat))) = N ) ) ).

tff(fact_1117_diff__Suc__less,axiom,
    ! [I_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(suc,I_2))),N)) ) ).

tff(fact_1118_gr0I,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ).

tff(fact_1119_diff__less__mono2,axiom,
    ! [L: nat,M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))) ) ) ).

tff(fact_1120_less__imp__diff__less,axiom,
    ! [N: nat,J: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J),N)),K_2)) ) ).

tff(fact_1121_gr__implies__not0,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ( N != zero_zero_nat ) ) ).

tff(fact_1122_diff__less,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M)) ) ) ).

tff(fact_1123_less__nat__zero__code,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).

tff(fact_1124_zero__less__diff,axiom,
    ! [N_2: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(N_2),M_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).

tff(fact_1125_neq0__conv,axiom,
    ! [N_2: nat] :
      ( ( N_2 != zero_zero_nat )
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) ) ).

tff(fact_1126_not__less0,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).

tff(fact_1127_less__eq__nat_Osimps_I1_J,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ).

tff(fact_1128_le__0__eq,axiom,
    ! [N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),zero_zero_nat))
    <=> ( N_2 = zero_zero_nat ) ) ).

tff(fact_1129_diff__le__self,axiom,
    ! [M: nat,N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M)) ).

tff(fact_1130_diff__is__0__eq,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ( hAPP_nat_nat(minus_minus_nat(M_2),N_2) = zero_zero_nat )
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).

tff(fact_1131_diff__is__0__eq_H,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => ( hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat ) ) ).

tff(fact_1132_diff__le__mono2,axiom,
    ! [L: nat,M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))) ) ).

tff(fact_1133_diff__le__mono,axiom,
    ! [L: nat,M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N),L))) ) ).

tff(fact_1134_diff__diff__cancel,axiom,
    ! [I_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N))
     => ( hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(minus_minus_nat(N),I_2)) = I_2 ) ) ).

tff(fact_1135_eq__diff__iff,axiom,
    ! [N_2: nat,K: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2))
       => ( ( hAPP_nat_nat(minus_minus_nat(M_2),K) = hAPP_nat_nat(minus_minus_nat(N_2),K) )
        <=> ( M_2 = N_2 ) ) ) ) ).

tff(fact_1136_Nat_Odiff__diff__eq,axiom,
    ! [N: nat,K_2: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N))
       => ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K_2)),hAPP_nat_nat(minus_minus_nat(N),K_2)) = hAPP_nat_nat(minus_minus_nat(M),N) ) ) ) ).

tff(fact_1137_le__diff__iff,axiom,
    ! [N_2: nat,K: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),K)),hAPP_nat_nat(minus_minus_nat(N_2),K)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ) ) ).

tff(fact_1138_Zero__not__Suc,axiom,
    ! [M: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,M) ) ).

tff(fact_1139_nat_Osimps_I2_J,axiom,
    ! [Nat_3: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,Nat_3) ) ).

tff(fact_1140_Suc__not__Zero,axiom,
    ! [M: nat] : ( hAPP_nat_nat(suc,M) != zero_zero_nat ) ).

tff(fact_1141_nat_Osimps_I3_J,axiom,
    ! [Nat_2: nat] : ( hAPP_nat_nat(suc,Nat_2) != zero_zero_nat ) ).

tff(fact_1142_diff__Suc__Suc,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(M),N) ) ).

tff(fact_1143_Suc__diff__diff,axiom,
    ! [M: nat,N: nat,K_2: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),K_2) ) ).

tff(fact_1144_Zero__neq__Suc,axiom,
    ! [M: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,M) ) ).

tff(fact_1145_Suc__neq__Zero,axiom,
    ! [M: nat] : ( hAPP_nat_nat(suc,M) != zero_zero_nat ) ).

tff(fact_1146_diffs0__imp__equal,axiom,
    ! [M: nat,N: nat] :
      ( ( hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat )
     => ( ( hAPP_nat_nat(minus_minus_nat(N),M) = zero_zero_nat )
       => ( M = N ) ) ) ).

tff(fact_1147_diff__commute,axiom,
    ! [I_2: nat,J: nat,K_2: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_2),J)),K_2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_2),K_2)),J) ) ).

tff(fact_1148_diff__self__eq__0,axiom,
    ! [M: nat] : ( hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat ) ).

tff(fact_1149_minus__nat_Odiff__0,axiom,
    ! [M: nat] : ( hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M ) ).

tff(fact_1150_diff__0__eq__0,axiom,
    ! [N: nat] : ( hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N) = zero_zero_nat ) ).

tff(fact_1151_diff__Suc,axiom,
    ! [M_2: nat,N_2: nat] : ( hAPP_nat_nat(minus_minus_nat(M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(minus_minus_nat(M_2),N_2)) ) ).

tff(fact_1152_diff__add__assoc2,axiom,
    ! [I_2: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J),I_2)),K_2) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J),K_2)),I_2) ) ) ).

tff(fact_1153_add__diff__assoc2,axiom,
    ! [I_2: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J),K_2)),I_2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J),I_2)),K_2) ) ) ).

tff(fact_1154_diff__add__assoc,axiom,
    ! [I_2: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_2),J)),K_2) = hAPP_nat_nat(plus_plus_nat(I_2),hAPP_nat_nat(minus_minus_nat(J),K_2)) ) ) ).

tff(fact_1155_le__imp__diff__is__add,axiom,
    ! [K: nat,I_1: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2))
     => ( ( hAPP_nat_nat(minus_minus_nat(J_2),I_1) = K )
      <=> ( J_2 = hAPP_nat_nat(plus_plus_nat(K),I_1) ) ) ) ).

tff(fact_1156_le__add__diff__inverse2,axiom,
    ! [N: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
     => ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),N) = M ) ) ).

tff(fact_1157_le__diff__conv2,axiom,
    ! [I_1: nat,K: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_2),K)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K)),J_2)) ) ) ).

tff(fact_1158_add__diff__assoc,axiom,
    ! [I_2: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(plus_plus_nat(I_2),hAPP_nat_nat(minus_minus_nat(J),K_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_2),J)),K_2) ) ) ).

tff(fact_1159_le__add__diff__inverse,axiom,
    ! [N: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
     => ( hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M ) ) ).

tff(fact_1160_le__add__diff,axiom,
    ! [M: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),K_2))) ) ).

tff(fact_1161_le__diff__conv,axiom,
    ! [J_2: nat,K: nat,I_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_2),K)),I_1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(plus_plus_nat(I_1),K))) ) ).

tff(fact_1162_diff__diff__right,axiom,
    ! [I_2: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(minus_minus_nat(I_2),hAPP_nat_nat(minus_minus_nat(J),K_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_2),K_2)),J) ) ) ).

tff(fact_1163_diff__less__mono,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C))) ) ) ).

tff(fact_1164_less__diff__iff,axiom,
    ! [N_2: nat,K: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_2),K)),hAPP_nat_nat(minus_minus_nat(N_2),K)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ) ) ).

tff(fact_1165_Suc__diff__le,axiom,
    ! [N: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
     => ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N)) ) ) ).

tff(fact_1166_less__diff__conv,axiom,
    ! [I_1: nat,J_2: nat,K: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_2),K)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K)),J_2)) ) ).

tff(fact_1167_add__diff__inverse,axiom,
    ! [M: nat,N: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ( hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M ) ) ).

tff(fact_1168_diff__less__Suc,axiom,
    ! [M: nat,N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),hAPP_nat_nat(suc,M))) ).

tff(fact_1169_less__Suc__eq__0__disj,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2)))
    <=> ( ( M_2 = zero_zero_nat )
        | ? [J_1: nat] :
            ( ( M_2 = hAPP_nat_nat(suc,J_1) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),N_2)) ) ) ) ).

tff(fact_1170_less__Suc0,axiom,
    ! [N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> ( N_2 = zero_zero_nat ) ) ).

tff(fact_1171_gr0__conv__Suc,axiom,
    ! [N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2))
    <=> ? [M_1: nat] : ( N_2 = hAPP_nat_nat(suc,M_1) ) ) ).

tff(fact_1172_one__is__add,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(M_2),N_2) )
    <=> ( ( ( M_2 = hAPP_nat_nat(suc,zero_zero_nat) )
          & ( N_2 = zero_zero_nat ) )
        | ( ( M_2 = zero_zero_nat )
          & ( N_2 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

tff(fact_1173_add__is__1,axiom,
    ! [M_2: nat,N_2: nat] :
      ( ( hAPP_nat_nat(plus_plus_nat(M_2),N_2) = hAPP_nat_nat(suc,zero_zero_nat) )
    <=> ( ( ( M_2 = hAPP_nat_nat(suc,zero_zero_nat) )
          & ( N_2 = zero_zero_nat ) )
        | ( ( M_2 = zero_zero_nat )
          & ( N_2 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

tff(fact_1174_add__gr__0,axiom,
    ! [M_2: nat,N_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(M_2),N_2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) ) ) ).

tff(fact_1175_min__Suc1,axiom,
    ! [N_2: nat,M_2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,N_2)),M_2) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(ord_min_nat,N_2))),M_2) ) ).

tff(fact_1176_min__Suc2,axiom,
    ! [M_2: nat,N_2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,ord_min_nat),N_2))),M_2) ) ).

tff(fact_1177_diff__Suc__diff__eq1,axiom,
    ! [M: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J),K_2))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K_2)),hAPP_nat_nat(suc,J)) ) ) ).

tff(fact_1178_diff__Suc__diff__eq2,axiom,
    ! [M: nat,K_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J))
     => ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J),K_2))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J)),hAPP_nat_nat(plus_plus_nat(K_2),M)) ) ) ).

tff(fact_1179_ex__least__nat__le,axiom,
    ! [N_2: nat,Pa: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,N_2))
       => ? [K_1: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_2))
            & ! [I: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1))
               => ~ hBOOL(hAPP_nat_bool(Pa,I)) )
            & hBOOL(hAPP_nat_bool(Pa,K_1)) ) ) ) ).

tff(fact_1180_less__imp__add__positive,axiom,
    ! [I_2: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
     => ? [K_1: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
          & ( hAPP_nat_nat(plus_plus_nat(I_2),K_1) = J ) ) ) ).

tff(fact_1181_gr0__implies__Suc,axiom,
    ! [N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ? [M_1: nat] : ( N = hAPP_nat_nat(suc,M_1) ) ) ).

tff(fact_1182_nat_Osize_I2_J,axiom,
    ! [Nat: nat] : ( hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) ) ).

tff(fact_1183_nat_Osize_I1_J,axiom,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat ).

tff(fact_1184_zero__induct__lemma,axiom,
    ! [I_1: nat,Pa: fun_nat_bool,K: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_1: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
           => hBOOL(hAPP_nat_bool(Pa,N_1)) )
       => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I_1))) ) ) ).

tff(fact_1185_not0__implies__Suc,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ? [M_1: nat] : ( N = hAPP_nat_nat(suc,M_1) ) ) ).

tff(fact_1186_nat__induct,axiom,
    ! [N_2: nat,Pa: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( ! [N_1: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,N_1))
           => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
       => hBOOL(hAPP_nat_bool(Pa,N_2)) ) ) ).

tff(fact_1187_nat_Oexhaust,axiom,
    ! [Y: nat] :
      ( ( Y != zero_zero_nat )
     => ~ ! [Nat_1: nat] : ( Y != hAPP_nat_nat(suc,Nat_1) ) ) ).

tff(fact_1188_zero__induct,axiom,
    ! [Pa: fun_nat_bool,K: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_1: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
           => hBOOL(hAPP_nat_bool(Pa,N_1)) )
       => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).

tff(fact_1189_nat_Osize_I4_J,axiom,
    ! [Nat: nat] : ( hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) ) ).

tff(fact_1190_nat_Osize_I3_J,axiom,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat ).

tff(fact_1191_nat__size,axiom,
    ! [N: nat] : ( hAPP_nat_nat(size_size_nat,N) = N ) ).

tff(fact_1192_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).

tff(fact_1193_Suc__eq__plus1,axiom,
    ! [N: nat] : ( hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(N),one_one_nat) ) ).

tff(fact_1194_Suc__eq__plus1__left,axiom,
    ! [N: nat] : ( hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N) ) ).

tff(fact_1195_diff__Suc__1,axiom,
    ! [N: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N)),one_one_nat) = N ) ).

tff(fact_1196_diff__Suc__eq__diff__pred,axiom,
    ! [M: nat,N: nat] : ( hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N) ) ).

tff(fact_1197_Suc__pred_H,axiom,
    ! [N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ( N = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N),one_one_nat)) ) ) ).

tff(fact_1198_Suc__diff__1,axiom,
    ! [N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ( hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N),one_one_nat)) = N ) ) ).

tff(fact_1199_add__eq__if,axiom,
    ! [N: nat,M: nat] :
      ( ( ( M = zero_zero_nat )
       => ( hAPP_nat_nat(plus_plus_nat(M),N) = N ) )
      & ( ( M != zero_zero_nat )
       => ( hAPP_nat_nat(plus_plus_nat(M),N) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N)) ) ) ) ).

%----Helper facts (144)
tff(help_fNot_1_1_U,axiom,
    ! [P: bool] :
      ( ~ hBOOL(hAPP_bool_bool(fNot,P))
      | ~ hBOOL(P) ) ).

tff(help_fNot_2_1_U,axiom,
    ! [P: bool] :
      ( hBOOL(P)
      | hBOOL(hAPP_bool_bool(fNot,P)) ) ).

tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fconj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(fconj(P),Q)) ) ).

tff(help_fconj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(fconj(P),Q))
      | hBOOL(P) ) ).

tff(help_fconj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(fconj(P),Q))
      | hBOOL(Q) ) ).

tff(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse) ).

tff(help_fFalse_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
    ! [P: nat] : ( hAPP_nat_nat(cOMBI_nat,P) = P ) ).

tff(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).

tff(help_fequal_1_1_fequal_000tc__HOL__Obool_T,axiom,
    ! [X: bool,Y: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__HOL__Obool_T,axiom,
    ! [X: bool,Y: bool] :
      ( ( X != Y )
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P: bool,Q: nat] : ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
    ! [P: fun_nat_nat,Q: fun_nat_nat,R: nat] : ( hAPP_nat_nat(hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,P),Q),R) = hAPP_nat_nat(P,hAPP_nat_nat(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
    ! [P: fun_nat_fun_nat_nat,Q: nat,R: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: nat,R: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P: fun_bool_bool,Q: fun_nat_bool,R: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_bool_bool,Q: fun_bool_bool,R: bool] : ( hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_bool_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_bo1549164019l_bool,Q: bool,R: bool] : ( hAPP_bool_bool(hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_b589554111l_bool(P,R),Q) ) ).

tff(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_T,axiom,
    ! [X: arrow_1893660431le_alt,Y: arrow_1893660431le_alt] :
      ( ~ hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(fequal1590852494le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_T,axiom,
    ! [X: arrow_1893660431le_alt,Y: arrow_1893660431le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(fequal1590852494le_alt,X),Y)) ) ).

tff(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_T,axiom,
    ! [X: arrow_856714788e_indi,Y: arrow_856714788e_indi] :
      ( ~ hBOOL(hAPP_A997847300i_bool(hAPP_A575544447i_bool(fequal1182599525e_indi,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_T,axiom,
    ! [X: arrow_856714788e_indi,Y: arrow_856714788e_indi] :
      ( ( X != Y )
      | hBOOL(hAPP_A997847300i_bool(hAPP_A575544447i_bool(fequal1182599525e_indi,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____eff,axiom,
    ! [P: bool,Q: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_b916665189t_bool(cOMBK_2077209654le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____eff_928,axiom,
    ! [P: bool,Q: arrow_856714788e_indi] : ( hAPP_A997847300i_bool(hAPP_b549570054i_bool(cOMBK_561380029e_indi,P),Q) = P ) ).

tff(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [X: list_A114658244le_alt,Y: list_A114658244le_alt] :
      ( ~ hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(fequal928191109le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [X: list_A114658244le_alt,Y: list_A114658244le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_l499746980t_bool(hAPP_l82091775t_bool(fequal928191109le_alt,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P: fun_na1436237685l_bool,Q: fun_nat_bool,R: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo492988759l_bool,Q: fun_bool_bool,R: bool] : ( hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order__,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar17477381t_bool,R: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_f1592536333t_bool(hAPP_f2127477477t_bool(cOMBB_388242475le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_A1748732503t_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order___929,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar1809396326i_bool,R: arrow_856714788e_indi] : ( hAPP_A997847300i_bool(hAPP_f1612707285i_bool(hAPP_f1347397683i_bool(cOMBB_1127256072e_indi,P),Q),R) = hAPP_bool_bool(P,hAPP_A997847300i_bool(Q,R)) ) ).

tff(help_fequal_1_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqb,axiom,
    ! [X: produc472769767le_alt,Y: produc472769767le_alt] :
      ( ~ hBOOL(hAPP_P1178790471t_bool(hAPP_P393387327t_bool(fequal346320936le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqb,axiom,
    ! [X: produc472769767le_alt,Y: produc472769767le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_P1178790471t_bool(hAPP_P393387327t_bool(fequal346320936le_alt,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t,axiom,
    ! [P: fun_Ar331856045t_bool,Q: arrow_1893660431le_alt,R: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(cOMBC_1826973210t_bool,P),Q),R) = hAPP_A1748732503t_bool(hAPP_A2063800319t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000,axiom,
    ! [P: fun_Ar14145203i_bool,Q: arrow_856714788e_indi,R: arrow_856714788e_indi] : ( hAPP_A997847300i_bool(hAPP_A575544447i_bool(hAPP_f512805993i_bool(cOMBC_1266306896i_bool,P),Q),R) = hAPP_A997847300i_bool(hAPP_A575544447i_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P: bool,Q: produc472769767le_alt] : ( hAPP_P1178790471t_bool(hAPP_b128655177t_bool(cOMBK_198697344le_alt,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____effn,axiom,
    ! [P: fun_na1003310479le_alt,Q: arrow_1893660431le_alt,R: nat] : ( hAPP_n2007559481le_alt(hAPP_A890253665le_alt(hAPP_f752897057le_alt(cOMBC_100033222le_alt,P),Q),R) = hAPP_A1382181054le_alt(hAPP_n1622045025le_alt(P,R),Q) ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: fun_Pr2067565481t_bool,Y: fun_Pr2067565481t_bool] :
      ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(fequal1830749992t_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: fun_Pr2067565481t_bool,Y: fun_Pr2067565481t_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(fequal1830749992t_bool,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_930,axiom,
    ! [P: fun_Ar569529141l_bool,Q: fun_Ar17477381t_bool,R: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_f1592536333t_bool(hAPP_f1090944335t_bool(cOMBC_1310341090l_bool,P),Q),R) = hAPP_f739344229l_bool(hAPP_A1501726285l_bool(P,R),Q) ) ).

tff(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: produc587761367le_alt,Y: produc587761367le_alt] : ( hAPP_P205052337le_alt(hAPP_P1755135161le_alt(if_Pro1687484775le_alt(fTrue),X),Y) = X ) ).

tff(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: produc587761367le_alt,Y: produc587761367le_alt] : ( hAPP_P205052337le_alt(hAPP_P1755135161le_alt(if_Pro1687484775le_alt(fFalse),X),Y) = Y ) ).

tff(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Arrow_,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr2067565481t_bool,R: produc472769767le_alt] : ( hAPP_P1178790471t_bool(hAPP_f1356305429t_bool(hAPP_f1645126899t_bool(cOMBB_325568203le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P1178790471t_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_931,axiom,
    ! [P: fun_Ar1047186533l_bool,Q: fun_Ar1809396326i_bool,R: arrow_856714788e_indi] : ( hAPP_A997847300i_bool(hAPP_f1612707285i_bool(hAPP_f1615874669i_bool(cOMBC_438428898l_bool,P),Q),R) = hAPP_f584385070l_bool(hAPP_A1597696899l_bool(P,R),Q) ) ).

tff(help_fequal_1_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab,axiom,
    ! [X: produc587761367le_alt,Y: produc587761367le_alt] :
      ( ~ hBOOL(hAPP_P1894408759t_bool(hAPP_P1907587391t_bool(fequal1054218392le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab,axiom,
    ! [X: produc587761367le_alt,Y: produc587761367le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_P1894408759t_bool(hAPP_P1907587391t_bool(fequal1054218392le_alt,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__prod_Itc,axiom,
    ! [P: fun_nat_bool,Q: produc472769767le_alt] : ( hAPP_P1123315306t_bool(hAPP_f795770633t_bool(cOMBK_1524165667le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: nat] : ( hAPP_n1161265524t_bool(hAPP_f1409698632t_bool(cOMBK_1882555695ol_nat,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,axiom,
    ! [P: fun_li90789869le_alt,Q: fun_na86871399le_alt,R: nat] : ( hAPP_n2007559481le_alt(hAPP_f2082356689le_alt(hAPP_f162101723le_alt(cOMBB_138440792lt_nat,P),Q),R) = hAPP_l84111627le_alt(P,hAPP_n2007559481le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____,axiom,
    ! [P: fun_na960272160le_alt,Q: list_A114658244le_alt,R: nat] : ( hAPP_n2007559481le_alt(hAPP_l1210406190le_alt(hAPP_f1096875589le_alt(cOMBC_869637379le_alt,P),Q),R) = hAPP_l84111627le_alt(hAPP_n372949560le_alt(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
    ! [P: bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f52567537l_bool(hAPP_b1272691967l_bool(cOMBK_81143760t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
    ! [P: fun_bool_bool,Q: produc472769767le_alt] : ( hAPP_P1103642805l_bool(hAPP_f699791347l_bool(cOMBK_138598520le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_932,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: bool] : ( hAPP_b128655177t_bool(hAPP_f1723896209t_bool(cOMBK_5056120l_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__prod_It,axiom,
    ! [P: fun_bool_bool,Q: fun_fu638310559l_bool,R: fun_Pr2067565481t_bool] : ( hAPP_f52567537l_bool(hAPP_f1060563265l_bool(hAPP_f1594093337l_bool(cOMBB_882486469t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f52567537l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P: fun_nat_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f703394068t_bool(hAPP_f779832389t_bool(cOMBK_198318445t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P: fun_fu638310559l_bool,Q: nat] : ( hAPP_n1134275860l_bool(hAPP_f1191475300l_bool(cOMBK_214082799ol_nat,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f463104139l_bool(hAPP_f1713038057l_bool(cOMBK_118864600t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_933,axiom,
    ! [P: fun_fu638310559l_bool,Q: bool] : ( hAPP_b1272691967l_bool(hAPP_f86272063l_bool(cOMBK_650639032l_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: fun_Ar245737999le_alt,R: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_f1490503959t_bool(hAPP_f1124798181t_bool(cOMBB_2030766369le_alt,P),Q),R) = hAPP_P1178790471t_bool(P,hAPP_A1299015393le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__List__,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr486337689t_bool,R: produc587761367le_alt] : ( hAPP_P1894408759t_bool(hAPP_f2146417685t_bool(hAPP_f202057843t_bool(cOMBB_1985622715le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P1894408759t_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,axiom,
    ! [P: fun_Ar17477381t_bool,Q: produc472769767le_alt] : ( hAPP_P1328248815t_bool(hAPP_f1074682185t_bool(cOMBK_385683240le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_934,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: arrow_1893660431le_alt] : ( hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(cOMBK_392407988le_alt,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_935,axiom,
    ! [P: fun_Ar1448189019le_alt,Q: list_A114658244le_alt,R: arrow_1893660431le_alt] : ( hAPP_A1382181054le_alt(hAPP_l1822938419le_alt(hAPP_f274624079le_alt(cOMBC_673369480le_alt,P),Q),R) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___936,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: produc472769767le_alt] : ( hAPP_P1859429372i_bool(hAPP_f359069313i_bool(cOMBK_1987648063le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_937,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: arrow_856714788e_indi] : ( hAPP_A1646126530t_bool(hAPP_f480276746t_bool(cOMBK_1650320063e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
    ! [P: fun_li90789869le_alt,Q: arrow_1893660431le_alt] : ( hAPP_A436723315le_alt(hAPP_f688183683le_alt(cOMBK_930998768le_alt,P),Q) = P ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs,axiom,
    ! [X: fun_Ar274636406t_bool,Y: fun_Ar274636406t_bool] :
      ( ~ hBOOL(hAPP_f995490902l_bool(hAPP_f2087119359l_bool(fequal957608631t_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs,axiom,
    ! [X: fun_Ar274636406t_bool,Y: fun_Ar274636406t_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f995490902l_bool(hAPP_f2087119359l_bool(fequal957608631t_bool,X),Y)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,axiom,
    ! [P: fun_fu1537843567t_bool,Q: fun_Ar331856045t_bool,R: arrow_1893660431le_alt] : ( hAPP_A2063800319t_bool(hAPP_f2095778909t_bool(hAPP_f1336702693t_bool(cOMBB_1074233563le_alt,P),Q),R) = hAPP_f1592536333t_bool(P,hAPP_A2063800319t_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_938,axiom,
    ! [P: fun_Ar339057223l_bool,Q: fun_Pr2067565481t_bool,R: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_f234621849t_bool(hAPP_f1689397393t_bool(cOMBC_395465908l_bool,P),Q),R) = hAPP_f52567537l_bool(hAPP_A442239897l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,axiom,
    ! [P: fun_li264309018le_alt,Q: list_A114658244le_alt,R: list_A114658244le_alt] : ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(hAPP_f204005175le_alt(cOMBC_1833749623le_alt,P),Q),R) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___939,axiom,
    ! [P: fun_Ar17477381t_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f234621849t_bool(hAPP_f1227262031t_bool(cOMBK_837265448t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_940,axiom,
    ! [P: fun_fu638310559l_bool,Q: arrow_1893660431le_alt] : ( hAPP_A442239897l_bool(hAPP_f1301449449l_bool(cOMBK_935799668le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: bool,Q: fun_Ar274636406t_bool] : ( hAPP_f995490902l_bool(hAPP_b1078573912l_bool(cOMBK_445086735t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___941,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f2010315474i_bool(hAPP_f1128827177i_bool(cOMBK_814147665t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_942,axiom,
    ! [P: fun_fu638310559l_bool,Q: arrow_856714788e_indi] : ( hAPP_A897398598l_bool(hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Arrow__,axiom,
    ! [P: fun_bool_bool,Q: fun_fu3835832l_bool,R: fun_Ar274636406t_bool] : ( hAPP_f995490902l_bool(hAPP_f819682389l_bool(hAPP_f1356804275l_bool(cOMBB_1044350042t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f995490902l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__943,axiom,
    ! [P: fun_nat_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f595382009t_bool(hAPP_f1195142808t_bool(cOMBK_155500978t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,axiom,
    ! [P: fun_fu3835832l_bool,Q: nat] : ( hAPP_n2125602947l_bool(hAPP_f784815496l_bool(cOMBK_238368224ol_nat,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_944,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1676084198l_bool(hAPP_f1582869284l_bool(cOMBK_542452487t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_945,axiom,
    ! [P: fun_fu3835832l_bool,Q: bool] : ( hAPP_b1078573912l_bool(hAPP_f1322579375l_bool(cOMBK_317366791l_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_946,axiom,
    ! [P: fun_Ar64685412t_bool,Q: arrow_1893660431le_alt,R: arrow_856714788e_indi] : ( hAPP_A1646126530t_bool(hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,P),Q),R) = hAPP_A1601437999t_bool(hAPP_A1309733808t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,axiom,
    ! [P: fun_Pr330364403t_bool,Q: produc472769767le_alt,R: produc472769767le_alt] : ( hAPP_P1178790471t_bool(hAPP_P393387327t_bool(hAPP_f1270778601t_bool(cOMBC_1805080534t_bool,P),Q),R) = hAPP_P1178790471t_bool(hAPP_P393387327t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_947,axiom,
    ! [P: fun_li143410744l_bool,Q: fun_Pr486337689t_bool,R: list_A114658244le_alt] : ( hAPP_l499746980t_bool(hAPP_f931065986t_bool(hAPP_f921473799t_bool(cOMBC_493955701l_bool,P),Q),R) = hAPP_f610613473l_bool(hAPP_l515395158l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_948,axiom,
    ! [P: fun_Ar636018671t_bool,Q: fun_Pr2067565481t_bool,R: arrow_1893660431le_alt] : ( hAPP_A2063800319t_bool(hAPP_f449303873t_bool(hAPP_f1081591777t_bool(cOMBC_557453916t_bool,P),Q),R) = hAPP_f234621849t_bool(hAPP_A656921921t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__949,axiom,
    ! [P: fun_Pr1085078251l_bool,Q: fun_Pr2067565481t_bool,R: produc472769767le_alt] : ( hAPP_P1178790471t_bool(hAPP_f1356305429t_bool(hAPP_f1033183015t_bool(cOMBC_593569186l_bool,P),Q),R) = hAPP_f52567537l_bool(hAPP_P38525833l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_950,axiom,
    ! [P: fun_li264309018le_alt,Q: fun_Ar849108972le_alt,R: arrow_1893660431le_alt] : ( hAPP_A436723315le_alt(hAPP_f218129964le_alt(hAPP_f757086845le_alt(cOMBB_1076781858le_alt,P),Q),R) = hAPP_l86320102le_alt(P,hAPP_A1382181054le_alt(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___951,axiom,
    ! [P: fun_Ar17477381t_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1841273342t_bool(hAPP_f1027939672t_bool(cOMBK_1334022583t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_952,axiom,
    ! [P: fun_fu3835832l_bool,Q: arrow_1893660431le_alt] : ( hAPP_A850178878l_bool(hAPP_f1173384643l_bool(cOMBK_757054181le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___953,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f391644589i_bool(hAPP_f2022065970i_bool(cOMBK_818801614t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_954,axiom,
    ! [P: fun_fu3835832l_bool,Q: arrow_856714788e_indi] : ( hAPP_A1411662545l_bool(hAPP_f1352816552l_bool(cOMBK_1255579598e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_955,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: produc587761367le_alt] : ( hAPP_P1708597583t_bool(hAPP_f1290118551t_bool(cOMBK_1555225330le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__,axiom,
    ! [P: fun_Pr486337689t_bool,Q: produc472769767le_alt] : ( hAPP_P588680495t_bool(hAPP_f480827367t_bool(cOMBK_605104626le_alt,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_956,axiom,
    ! [P: fun_li47571840le_alt,Q: fun_li90789869le_alt,R: list_A114658244le_alt] : ( hAPP_l1580775710le_alt(hAPP_f200431784le_alt(hAPP_f416142309le_alt(cOMBB_250395785le_alt,P),Q),R) = hAPP_l1580775710le_alt(P,hAPP_l84111627le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [P: fun_fu643206625l_bool,Q: fun_Pr2067565481t_bool,R: fun_Pr2067565481t_bool] : ( hAPP_f52567537l_bool(hAPP_f930900275l_bool(hAPP_f599780549l_bool(cOMBC_1554707866l_bool,P),Q),R) = hAPP_f52567537l_bool(hAPP_f930900275l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___957,axiom,
    ! [P: fun_fu372082297t_bool,Q: fun_Ar2121501495le_alt,R: arrow_1893660431le_alt] : ( hAPP_A2063800319t_bool(hAPP_f783327207t_bool(hAPP_f404316901t_bool(cOMBB_1598772817le_alt,P),Q),R) = hAPP_f1490503959t_bool(P,hAPP_A1146194953le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_958,axiom,
    ! [P: fun_Ar290235730t_bool,Q: arrow_1893660431le_alt,R: arrow_856714788e_indi] : ( hAPP_A1309733808t_bool(hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,P),Q),R) = hAPP_A1058422557t_bool(hAPP_A38124190t_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_959,axiom,
    ! [P: fun_fu638310559l_bool,Q: produc587761367le_alt] : ( hAPP_P171164537l_bool(hAPP_f908691129l_bool(cOMBK_1807543090le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___960,axiom,
    ! [P: fun_Pr486337689t_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f369701637t_bool(hAPP_f1369154921t_bool(cOMBK_1697579230t_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_Pr1025510259t_bool,Q: produc587761367le_alt,R: produc587761367le_alt] : ( hAPP_P1894408759t_bool(hAPP_P1907587391t_bool(hAPP_f870273001t_bool(cOMBC_2103205814t_bool,P),Q),R) = hAPP_P1894408759t_bool(hAPP_P1907587391t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_961,axiom,
    ! [P: fun_fu864675765l_bool,Q: fun_fu638310559l_bool,R: fun_Pr2067565481t_bool] : ( hAPP_f52567537l_bool(hAPP_f1060563265l_bool(hAPP_f1776355587l_bool(cOMBC_2133093654l_bool,P),Q),R) = hAPP_f182583295l_bool(hAPP_f1482930381l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__962,axiom,
    ! [P: fun_Pr1085078251l_bool,Q: fun_Ar245737999le_alt,R: arrow_1893660431le_alt] : ( hAPP_A442239897l_bool(hAPP_f1536341593l_bool(hAPP_f1344055909l_bool(cOMBB_1660064607le_alt,P),Q),R) = hAPP_P38525833l_bool(P,hAPP_A1299015393le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_963,axiom,
    ! [P: fun_li359495831t_bool,Q: fun_Pr486337689t_bool,R: list_A114658244le_alt] : ( hAPP_l82091775t_bool(hAPP_f1232688951t_bool(hAPP_f1613523967t_bool(cOMBC_1701707246t_bool,P),Q),R) = hAPP_f931065986t_bool(hAPP_l706029667t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_964,axiom,
    ! [P: fun_Pr2124911691l_bool,Q: fun_Pr486337689t_bool,R: produc587761367le_alt] : ( hAPP_P1894408759t_bool(hAPP_f2146417685t_bool(hAPP_f1616253255t_bool(cOMBC_1249985698l_bool,P),Q),R) = hAPP_f610613473l_bool(hAPP_P489291369l_bool(P,R),Q) ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____e,axiom,
    ! [X: fun_fu2114379172t_bool,Y: fun_fu2114379172t_bool] :
      ( ~ hBOOL(hAPP_f1572141188l_bool(hAPP_f1105736319l_bool(fequal1249241829t_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____e,axiom,
    ! [X: fun_fu2114379172t_bool,Y: fun_fu2114379172t_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f1572141188l_bool(hAPP_f1105736319l_bool(fequal1249241829t_bool,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
    ! [P: bool,Q: fun_fu2114379172t_bool] : ( hAPP_f1572141188l_bool(hAPP_b1777246598l_bool(cOMBK_1279003709t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_965,axiom,
    ! [P: fun_fu638310559l_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1915815064l_bool(hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_966,axiom,
    ! [P: fun_li380014893le_alt,Q: fun_li90789869le_alt,R: list_A114658244le_alt] : ( hAPP_l660415097le_alt(hAPP_f1274386949le_alt(hAPP_f1142066787le_alt(cOMBB_1071360260le_alt,P),Q),R) = hAPP_l660415097le_alt(P,hAPP_l84111627le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_Pr1186243091le_alt,Q: fun_li47571840le_alt,R: list_A114658244le_alt] : ( hAPP_l1580775710le_alt(hAPP_f739355093le_alt(hAPP_f635935679le_alt(cOMBB_1945714076le_alt,P),Q),R) = hAPP_P205052337le_alt(P,hAPP_l1580775710le_alt(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn,axiom,
    ! [P: fun_li101108800le_alt,Q: fun_li47571840le_alt,R: list_A114658244le_alt] : ( hAPP_l1580775710le_alt(hAPP_f739355093le_alt(hAPP_f579647290le_alt(cOMBS_19686701le_alt,P),Q),R) = hAPP_P205052337le_alt(hAPP_l859329548le_alt(P,R),hAPP_l1580775710le_alt(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_967,axiom,
    ! [P: fun_fu3835832l_bool,Q: produc587761367le_alt] : ( hAPP_P878768990l_bool(hAPP_f1465094837l_bool(cOMBK_448375169le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___968,axiom,
    ! [P: fun_Pr486337689t_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1745861984t_bool(hAPP_f2020753944t_bool(cOMBK_342345345t_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc,axiom,
    ! [P: fun_bool_bool,Q: fun_fu2098777574l_bool,R: fun_fu2114379172t_bool] : ( hAPP_f1572141188l_bool(hAPP_f1181604821l_bool(hAPP_f1662395443l_bool(cOMBB_1112311688t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f1572141188l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__969,axiom,
    ! [P: fun_nat_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f1550778407t_bool(hAPP_f1319616198t_bool(cOMBK_2008571104t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_fu2098777574l_bool,Q: nat] : ( hAPP_n1555388849l_bool(hAPP_f1268543752l_bool(cOMBK_1485688882ol_nat,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_970,axiom,
    ! [P: fun_bool_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f414129720l_bool(hAPP_f1152234870l_bool(cOMBK_1770320693t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_971,axiom,
    ! [P: fun_fu2098777574l_bool,Q: bool] : ( hAPP_b1777246598l_bool(hAPP_f369767947l_bool(cOMBK_2030738485l_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,axiom,
    ! [P: fun_fu257364531l_bool,Q: fun_Ar274636406t_bool,R: fun_Ar274636406t_bool] : ( hAPP_f995490902l_bool(hAPP_f2087119359l_bool(hAPP_f410199913l_bool(cOMBC_353845492l_bool,P),Q),R) = hAPP_f995490902l_bool(hAPP_f2087119359l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_972,axiom,
    ! [P: fun_Pr2124911691l_bool,Q: fun_li47571840le_alt,R: list_A114658244le_alt] : ( hAPP_l515395158l_bool(hAPP_f1223082253l_bool(hAPP_f1589431871l_bool(cOMBB_835145300le_alt,P),Q),R) = hAPP_P489291369l_bool(P,hAPP_l1580775710le_alt(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___973,axiom,
    ! [P: fun_Ar17477381t_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f2038412844t_bool(hAPP_f1552202630t_bool(cOMBK_1544325605t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_974,axiom,
    ! [P: fun_fu2098777574l_bool,Q: arrow_1893660431le_alt] : ( hAPP_A1569148780l_bool(hAPP_f1933295939l_bool(cOMBK_1583688247le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___975,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f399308031i_bool(hAPP_f448050564i_bool(cOMBK_443335420t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_976,axiom,
    ! [P: fun_fu2098777574l_bool,Q: arrow_856714788e_indi] : ( hAPP_A2084592127l_bool(hAPP_f258290692l_bool(cOMBK_1514079484e_indi,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___977,axiom,
    ! [P: fun_fu361117961l_bool,Q: fun_fu3835832l_bool,R: fun_Ar274636406t_bool] : ( hAPP_f995490902l_bool(hAPP_f819682389l_bool(hAPP_f1760776521l_bool(cOMBC_514203746l_bool,P),Q),R) = hAPP_f73423488l_bool(hAPP_f1225332775l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_978,axiom,
    ! [P: fun_li967808957le_alt,Q: fun_li90789869le_alt,R: list_A114658244le_alt] : ( hAPP_l660415097le_alt(hAPP_f1274386949le_alt(hAPP_f905689843le_alt(cOMBC_1284478484le_alt,P),Q),R) = hAPP_f200431784le_alt(hAPP_l1263040137le_alt(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___979,axiom,
    ! [P: fun_fu1572237755l_bool,Q: fun_Ar2121501495le_alt,R: arrow_1893660431le_alt] : ( hAPP_A1608658241l_bool(hAPP_f184584489l_bool(hAPP_f759033445l_bool(cOMBB_1575576719le_alt,P),Q),R) = hAPP_f1536341593l_bool(P,hAPP_A1146194953le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [P: fun_fu1287834969t_bool,Q: fun_Ar274636406t_bool,R: arrow_856714788e_indi] : ( hAPP_A38124190t_bool(hAPP_f1751344075t_bool(hAPP_f908467689t_bool(cOMBB_1876517692e_indi,P),Q),R) = hAPP_f1550387441t_bool(P,hAPP_A1646126530t_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___980,axiom,
    ! [P: fun_fu696673523t_bool,Q: fun_Ar1995913199l_bool,R: arrow_1893660431le_alt] : ( hAPP_A656921921t_bool(hAPP_f105674721t_bool(hAPP_f322072549t_bool(cOMBB_652885079le_alt,P),Q),R) = hAPP_f1689397393t_bool(P,hAPP_A1608658241l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_981,axiom,
    ! [P: fun_fu2098777574l_bool,Q: produc587761367le_alt] : ( hAPP_P1986703244l_bool(hAPP_f852696849l_bool(cOMBK_1524832687le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___982,axiom,
    ! [P: fun_Pr486337689t_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f210821554t_bool(hAPP_f2065367146t_bool(cOMBK_1118451887t_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
    ! [P: fun_fu244651069le_alt,Q: fun_li380014893le_alt,R: list_A114658244le_alt] : ( hAPP_l660415097le_alt(hAPP_f6098781le_alt(hAPP_f533347863le_alt(cOMBB_1792551872le_alt,P),Q),R) = hAPP_f739355093le_alt(P,hAPP_l660415097le_alt(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____effn_983,axiom,
    ! [P: fun_li1530812010le_alt,Q: fun_li380014893le_alt,R: list_A114658244le_alt] : ( hAPP_l660415097le_alt(hAPP_f6098781le_alt(hAPP_f423920914le_alt(cOMBS_917035857le_alt,P),Q),R) = hAPP_f739355093le_alt(hAPP_l384915638le_alt(P,R),hAPP_l660415097le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_984,axiom,
    ! [P: fun_Pr544315117le_alt,Q: fun_li47571840le_alt,R: list_A114658244le_alt] : ( hAPP_l859329548le_alt(hAPP_f1737347755le_alt(hAPP_f1372126793le_alt(cOMBB_730268484le_alt,P),Q),R) = hAPP_P1755135161le_alt(P,hAPP_l1580775710le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_985,axiom,
    ! [P: fun_fu976291829l_bool,Q: fun_li380014893le_alt,R: list_A114658244le_alt] : ( hAPP_l776557489l_bool(hAPP_f561566485l_bool(hAPP_f1983518615l_bool(cOMBB_1429729016le_alt,P),Q),R) = hAPP_f1223082253l_bool(P,hAPP_l660415097le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_986,axiom,
    ! [P: fun_fu1919656431t_bool,Q: fun_li312794341l_bool,R: list_A114658244le_alt] : ( hAPP_l706029667t_bool(hAPP_f406989951t_bool(hAPP_f2107183495t_bool(cOMBB_2102331378le_alt,P),Q),R) = hAPP_f921473799t_bool(P,hAPP_l776557489l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_987,axiom,
    ! [P: fun_fu994968269le_alt,Q: fun_li380014893le_alt,R: list_A114658244le_alt] : ( hAPP_l1263040137le_alt(hAPP_f1148079597le_alt(hAPP_f1250095511le_alt(cOMBB_1247716816le_alt,P),Q),R) = hAPP_f416142309le_alt(P,hAPP_l660415097le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_988,axiom,
    ! [P: fun_fu1286404697le_alt,Q: fun_li380014893le_alt,R: list_A114658244le_alt] : ( hAPP_l1985992967le_alt(hAPP_f1455388473le_alt(hAPP_f1097645385le_alt(cOMBB_1772667958le_alt,P),Q),R) = hAPP_f1737347755le_alt(P,hAPP_l660415097le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,axiom,
    ! [P: fun_fu1441209011l_bool,Q: fun_fu2114379172t_bool,R: fun_fu2114379172t_bool] : ( hAPP_f1572141188l_bool(hAPP_f1105736319l_bool(hAPP_f1764760681l_bool(cOMBC_57903184l_bool,P),Q),R) = hAPP_f1572141188l_bool(hAPP_f1105736319l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_989,axiom,
    ! [P: fun_fu1383920485l_bool,Q: fun_fu2098777574l_bool,R: fun_fu2114379172t_bool] : ( hAPP_f1572141188l_bool(hAPP_f1181604821l_bool(hAPP_f1169241965l_bool(cOMBC_1209358050l_bool,P),Q),R) = hAPP_f975209902l_bool(hAPP_f1714503811l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_990,axiom,
    ! [P: fun_fu153784302le_alt,Q: fun_li2074124649le_alt,R: list_A114658244le_alt] : ( hAPP_l384915638le_alt(hAPP_f1967789246le_alt(hAPP_f752890973le_alt(cOMBB_1206549317le_alt,P),Q),R) = hAPP_f579647290le_alt(P,hAPP_l1985992967le_alt(Q,R)) ) ).

%----Conjectures (1)
% tff(conj_0,conjecture,
%     ! [I: arrow_856714788e_indi] :
%       ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,I)))
%     <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,I)),c),b))) ) ).

%------------------------------------------------------------------------------